https://groupprops.subwiki.org/wiki/Special:ExportRDF/Category-3ASubgroup_property_non-2Dimplications
type: Ontology
creation date: 2026-01-13T17:29:28+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Subgroup property non-implications
type: Class
page: https://groupprops.subwiki.org/wiki/Category-3ASubgroup_property_non-2Dimplications
wiki namespace: 14
wiki page content language: en
wiki page modification date: 2008-05-07T22:39:23Z
modification date#aux: 2454594.4440162
wiki page sort key: Subgroup property non-implications
subclass of: Category:Property non-implications

Characteristic not implies powering-invariant in nilpotent group
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_powering-2Dinvariant_in_nilpotent_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies powering-invariant in nilpotent group

Normal not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies characteristic

Descendant not implies subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Descendant_not_implies_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Descendant not implies subnormal

Ascendant not implies subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Ascendant_not_implies_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ascendant not implies subnormal

Normal not implies left-transitively fixed-depth subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_left-2Dtransitively_fixed-2Ddepth_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies left-transitively fixed-depth subnormal

Normal not implies right-transitively fixed-depth subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_right-2Dtransitively_fixed-2Ddepth_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies right-transitively fixed-depth subnormal

Nilpotent not implies ACIC
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_not_implies_ACIC
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nilpotent not implies ACIC

Hall not implies pronormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Hall_not_implies_pronormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Hall not implies pronormal

Hall not implies order-conjugate
type: Subject
page: https://groupprops.subwiki.org/wiki/Hall_not_implies_order-2Dconjugate
wiki namespace: 0
wiki page content language: en
wiki page sort key: Hall not implies order-conjugate

Normal not implies strongly potentially characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_strongly_potentially_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies strongly potentially characteristic

Normal not implies normal-potentially characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_normal-2Dpotentially_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies normal-potentially characteristic

Hall not implies WNSCDIN
type: Subject
page: https://groupprops.subwiki.org/wiki/Hall_not_implies_WNSCDIN
wiki namespace: 0
wiki page content language: en
wiki page sort key: Hall not implies WNSCDIN

Pronormal not implies NE
type: Subject
page: https://groupprops.subwiki.org/wiki/Pronormal_not_implies_NE
wiki namespace: 0
wiki page content language: en
wiki page sort key: Pronormal not implies NE

Sylow not implies NE
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_not_implies_NE
wiki namespace: 0
wiki page content language: en
wiki page sort key: Sylow not implies NE

Subnormal not implies conjugate-permutable
type: Subject
page: https://groupprops.subwiki.org/wiki/Subnormal_not_implies_conjugate-2Dpermutable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subnormal not implies conjugate-permutable

Order-conjugate and Hall not implies order-dominating
type: Subject
page: https://groupprops.subwiki.org/wiki/Order-2Dconjugate_and_Hall_not_implies_order-2Ddominating
wiki namespace: 0
wiki page content language: en
wiki page sort key: Order-conjugate and Hall not implies order-dominating

Left-transitively WNSCDIN not implies normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Left-2Dtransitively_WNSCDIN_not_implies_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Left-transitively WNSCDIN not implies normal

Left-transitively homomorph-containing not implies subhomomorph-containing
type: Subject
page: https://groupprops.subwiki.org/wiki/Left-2Dtransitively_homomorph-2Dcontaining_not_implies_subhomomorph-2Dcontaining
wiki namespace: 0
wiki page content language: en
wiki page sort key: Left-transitively homomorph-containing not implies subhomomorph-containing

Strictly characteristic not implies fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Strictly_characteristic_not_implies_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Strictly characteristic not implies fully invariant

Locally inner automorphism-balanced not implies central factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Locally_inner_automorphism-2Dbalanced_not_implies_central_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally inner automorphism-balanced not implies central factor

Conjugacy-closed normal not implies central factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Conjugacy-2Dclosed_normal_not_implies_central_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Conjugacy-closed normal not implies central factor

Permutable not implies normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Permutable_not_implies_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Permutable not implies normal

Potentially characteristic not implies characteristic-potentially characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Potentially_characteristic_not_implies_characteristic-2Dpotentially_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Potentially characteristic not implies characteristic-potentially characteristic

Potentially characteristic not implies normal-potentially characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Potentially_characteristic_not_implies_normal-2Dpotentially_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Potentially characteristic not implies normal-potentially characteristic

Potentially characteristic not implies normal-extensible automorphism-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Potentially_characteristic_not_implies_normal-2Dextensible_automorphism-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Potentially characteristic not implies normal-extensible automorphism-invariant

Verbal not implies commutator-verbal
type: Subject
page: https://groupprops.subwiki.org/wiki/Verbal_not_implies_commutator-2Dverbal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Verbal not implies commutator-verbal

No common composition factor with quotient group not implies complemented
type: Subject
page: https://groupprops.subwiki.org/wiki/No_common_composition_factor_with_quotient_group_not_implies_complemented
wiki namespace: 0
wiki page content language: en
wiki page sort key: No common composition factor with quotient group not implies complemented

Subnormal not implies normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Subnormal_not_implies_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subnormal not implies normal

Automorph-permutable not implies permutable
type: Subject
page: https://groupprops.subwiki.org/wiki/Automorph-2Dpermutable_not_implies_permutable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Automorph-permutable not implies permutable

Conjugacy-closed and Hall not implies retract
type: Subject
page: https://groupprops.subwiki.org/wiki/Conjugacy-2Dclosed_and_Hall_not_implies_retract
wiki namespace: 0
wiki page content language: en
wiki page sort key: Conjugacy-closed and Hall not implies retract

No nontrivial homomorphism to quotient group not implies complemented normal
type: Subject
page: https://groupprops.subwiki.org/wiki/No_nontrivial_homomorphism_to_quotient_group_not_implies_complemented_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: No nontrivial homomorphism to quotient group not implies complemented normal

Subisomorph-containing not implies homomorph-containing
type: Subject
page: https://groupprops.subwiki.org/wiki/Subisomorph-2Dcontaining_not_implies_homomorph-2Dcontaining
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subisomorph-containing not implies homomorph-containing

Cocentral not implies amalgam-characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Cocentral_not_implies_amalgam-2Dcharacteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Cocentral not implies amalgam-characteristic

Characteristic not implies strictly characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_strictly_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies strictly characteristic

Order-conjugate and Hall not implies order-dominated
type: Subject
page: https://groupprops.subwiki.org/wiki/Order-2Dconjugate_and_Hall_not_implies_order-2Ddominated
wiki namespace: 0
wiki page content language: en
wiki page sort key: Order-conjugate and Hall not implies order-dominated

Subgroup of abelian group not implies abelian-extensible automorphism-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroup_of_abelian_group_not_implies_abelian-2Dextensible_automorphism-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subgroup of abelian group not implies abelian-extensible automorphism-invariant

Weakly normal not implies NE
type: Subject
page: https://groupprops.subwiki.org/wiki/Weakly_normal_not_implies_NE
wiki namespace: 0
wiki page content language: en
wiki page sort key: Weakly normal not implies NE

2-subnormal not implies hypernormalized
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_not_implies_hypernormalized
wiki namespace: 0
wiki page content language: en
wiki page sort key: 2-subnormal not implies hypernormalized

Quotient group need not be isomorphic to any subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Quotient_group_need_not_be_isomorphic_to_any_subgroup
wiki namespace: 0
wiki page content language: en
wiki page sort key: Quotient group need not be isomorphic to any subgroup

Normal not implies amalgam-characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_amalgam-2Dcharacteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies amalgam-characteristic

Normal not implies potentially verbal
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_potentially_verbal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies potentially verbal

Characteristic not implies potentially fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_potentially_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies potentially fully invariant

Normal not implies potentially fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_potentially_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies potentially fully invariant

Characteristic not implies amalgam-characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_amalgam-2Dcharacteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies amalgam-characteristic

Characteristic not implies fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies fully invariant

Iterated agemo subgroup not implies agemo subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Iterated_agemo_subgroup_not_implies_agemo_subgroup
wiki namespace: 0
wiki page content language: en
wiki page sort key: Iterated agemo subgroup not implies agemo subgroup

Image-closed characteristic not implies fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Image-2Dclosed_characteristic_not_implies_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Image-closed characteristic not implies fully invariant

Abnormal normalizer not implies pronormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Abnormal_normalizer_not_implies_pronormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abnormal normalizer not implies pronormal

Fusion system-relatively weakly closed not implies isomorph-normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Fusion_system-2Drelatively_weakly_closed_not_implies_isomorph-2Dnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Fusion system-relatively weakly closed not implies isomorph-normal

2-subnormal not implies automorph-permutable
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_not_implies_automorph-2Dpermutable
wiki namespace: 0
wiki page content language: en
wiki page sort key: 2-subnormal not implies automorph-permutable

Finite direct power-closed characteristic not implies fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_direct_power-2Dclosed_characteristic_not_implies_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite direct power-closed characteristic not implies fully invariant

Right-transitively homomorph-containing not implies subhomomorph-containing
type: Subject
page: https://groupprops.subwiki.org/wiki/Right-2Dtransitively_homomorph-2Dcontaining_not_implies_subhomomorph-2Dcontaining
wiki namespace: 0
wiki page content language: en
wiki page sort key: Right-transitively homomorph-containing not implies subhomomorph-containing

Complemented central factor not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Complemented_central_factor_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complemented central factor not implies direct factor

Normal-extensible not implies inner
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal-2Dextensible_not_implies_inner
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal-extensible not implies inner

Finite not implies divisibility-closed in abelian group
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_not_implies_divisibility-2Dclosed_in_abelian_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite not implies divisibility-closed in abelian group

Characteristic not implies quasiautomorphism-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_quasiautomorphism-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies quasiautomorphism-invariant

Finite solvable not implies p-normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_solvable_not_implies_p-2Dnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite solvable not implies p-normal

Homomorph-containing not implies no nontrivial homomorphism to quotient group
type: Subject
page: https://groupprops.subwiki.org/wiki/Homomorph-2Dcontaining_not_implies_no_nontrivial_homomorphism_to_quotient_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Homomorph-containing not implies no nontrivial homomorphism to quotient group

Transitively normal not implies central factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Transitively_normal_not_implies_central_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Transitively normal not implies central factor

Local powering-invariant not implies local divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Local_powering-2Dinvariant_not_implies_local_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Local powering-invariant not implies local divisibility-closed

Normal not implies normal-potentially relatively characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_normal-2Dpotentially_relatively_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies normal-potentially relatively characteristic

Characteristic not implies injective endomorphism-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_injective_endomorphism-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies injective endomorphism-invariant

Normal-potentially characteristic not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal-2Dpotentially_characteristic_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal-potentially characteristic not implies characteristic

Normal not implies central factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_central_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies central factor

Sylow not implies local divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_not_implies_local_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Sylow not implies local divisibility-closed

Characteristic-isomorph-free not implies normal-isomorph-free in finite
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic-2Disomorph-2Dfree_not_implies_normal-2Disomorph-2Dfree_in_finite
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic-isomorph-free not implies normal-isomorph-free in finite

Endomorphism kernel not implies complemented normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Endomorphism_kernel_not_implies_complemented_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Endomorphism kernel not implies complemented normal

Fully invariant subgroup of abelian group not implies divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Fully_invariant_subgroup_of_abelian_group_not_implies_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Fully invariant subgroup of abelian group not implies divisibility-closed

Sylow not implies CDIN
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_not_implies_CDIN
wiki namespace: 0
wiki page content language: en
wiki page sort key: Sylow not implies CDIN

Powering-invariance does not satisfy lower central series condition in nilpotent group
type: Subject
page: https://groupprops.subwiki.org/wiki/Powering-2Dinvariance_does_not_satisfy_lower_central_series_condition_in_nilpotent_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Powering-invariance does not satisfy lower central series condition in nilpotent group

Subgroup of abelian group not implies abelian-potentially characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroup_of_abelian_group_not_implies_abelian-2Dpotentially_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subgroup of abelian group not implies abelian-potentially characteristic

Normal not implies image-potentially fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_image-2Dpotentially_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies image-potentially fully invariant

Conjugate-comparable not implies normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Conjugate-2Dcomparable_not_implies_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Conjugate-comparable not implies normal

Characteristic subgroup of abelian group not implies local powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_subgroup_of_abelian_group_not_implies_local_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic subgroup of abelian group not implies local powering-invariant

Powering-invariant not implies local powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Powering-2Dinvariant_not_implies_local_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Powering-invariant not implies local powering-invariant

Lattice-complemented not implies permutably complemented
type: Subject
page: https://groupprops.subwiki.org/wiki/Lattice-2Dcomplemented_not_implies_permutably_complemented
wiki namespace: 0
wiki page content language: en
wiki page sort key: Lattice-complemented not implies permutably complemented

Verbal subgroup of abelian group not implies local powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Verbal_subgroup_of_abelian_group_not_implies_local_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Verbal subgroup of abelian group not implies local powering-invariant

Order-conjugate not implies order-dominating
type: Subject
page: https://groupprops.subwiki.org/wiki/Order-2Dconjugate_not_implies_order-2Ddominating
wiki namespace: 0
wiki page content language: en
wiki page sort key: Order-conjugate not implies order-dominating

Normal-extensible not implies normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal-2Dextensible_not_implies_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal-extensible not implies normal

Verbal not implies iterated agemo
type: Subject
page: https://groupprops.subwiki.org/wiki/Verbal_not_implies_iterated_agemo
wiki namespace: 0
wiki page content language: en
wiki page sort key: Verbal not implies iterated agemo

Central factor not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Central_factor_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Central factor not implies direct factor

Normal-isomorph-free not implies isomorph-free in finite
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal-2Disomorph-2Dfree_not_implies_isomorph-2Dfree_in_finite
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal-isomorph-free not implies isomorph-free in finite

Image-closed fully invariant not implies verbal
type: Subject
page: https://groupprops.subwiki.org/wiki/Image-2Dclosed_fully_invariant_not_implies_verbal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Image-closed fully invariant not implies verbal

3-subnormal not implies finite-automorph-join-closed subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/3-2Dsubnormal_not_implies_finite-2Dautomorph-2Djoin-2Dclosed_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: 3-subnormal not implies finite-automorph-join-closed subnormal

Characteristic subgroup of abelian group not implies divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_subgroup_of_abelian_group_not_implies_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic subgroup of abelian group not implies divisibility-closed

Direct factor not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_factor_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Direct factor not implies characteristic

Paranormal not implies pronormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Paranormal_not_implies_pronormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Paranormal not implies pronormal

Abelian normal not implies central
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian_normal_not_implies_central
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abelian normal not implies central

Contranormal not implies self-normalizing
type: Subject
page: https://groupprops.subwiki.org/wiki/Contranormal_not_implies_self-2Dnormalizing
wiki namespace: 0
wiki page content language: en
wiki page sort key: Contranormal not implies self-normalizing

Normal not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normal not implies direct factor

Complemented characteristic not implies left-transitively complemented normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Complemented_characteristic_not_implies_left-2Dtransitively_complemented_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complemented characteristic not implies left-transitively complemented normal

Divisibility-closed not implies local divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Divisibility-2Dclosed_not_implies_local_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Divisibility-closed not implies local divisibility-closed

Index two not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Index_two_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Index two not implies characteristic

Existentially bound-word not implies verbal
type: Subject
page: https://groupprops.subwiki.org/wiki/Existentially_bound-2Dword_not_implies_verbal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Existentially bound-word not implies verbal

Complemented normal not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Complemented_normal_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complemented normal not implies direct factor

P-automorphism-invariant not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/P-2Dautomorphism-2Dinvariant_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: P-automorphism-invariant not implies characteristic

Characteristic direct factor not implies fully invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_direct_factor_not_implies_fully_invariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic direct factor not implies fully invariant

Powering-invariant not implies divisibility-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Powering-2Dinvariant_not_implies_divisibility-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Powering-invariant not implies divisibility-closed

Endomorph-dominating not implies automorph-conjugate
type: Subject
page: https://groupprops.subwiki.org/wiki/Endomorph-2Ddominating_not_implies_automorph-2Dconjugate
wiki namespace: 0
wiki page content language: en
wiki page sort key: Endomorph-dominating not implies automorph-conjugate

Finite index not implies local powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_index_not_implies_local_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite index not implies local powering-invariant

1-closed transversal not implies permutably complemented
type: Subject
page: https://groupprops.subwiki.org/wiki/1-2Dclosed_transversal_not_implies_permutably_complemented
wiki namespace: 0
wiki page content language: en
wiki page sort key: 1-closed transversal not implies permutably complemented

Order-conjugate not implies order-dominated
type: Subject
page: https://groupprops.subwiki.org/wiki/Order-2Dconjugate_not_implies_order-2Ddominated
wiki namespace: 0
wiki page content language: en
wiki page sort key: Order-conjugate not implies order-dominated

Characteristic not implies characteristic-isomorph-free in finite
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_characteristic-2Disomorph-2Dfree_in_finite
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies characteristic-isomorph-free in finite

Subhomomorph-containing not implies variety-containing
type: Subject
page: https://groupprops.subwiki.org/wiki/Subhomomorph-2Dcontaining_not_implies_variety-2Dcontaining
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subhomomorph-containing not implies variety-containing

Subgroup of abelian group not implies powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroup_of_abelian_group_not_implies_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subgroup of abelian group not implies powering-invariant

Characteristic not implies elementarily characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_elementarily_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies elementarily characteristic

Powering-invariant and normal not implies quotient-powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Powering-2Dinvariant_and_normal_not_implies_quotient-2Dpowering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Powering-invariant and normal not implies quotient-powering-invariant

Base of a wreath product not implies elliptic
type: Subject
page: https://groupprops.subwiki.org/wiki/Base_of_a_wreath_product_not_implies_elliptic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Base of a wreath product not implies elliptic

Conjugacy-closed not implies weak subset-conjugacy-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/Conjugacy-2Dclosed_not_implies_weak_subset-2Dconjugacy-2Dclosed
wiki namespace: 0
wiki page content language: en
wiki page sort key: Conjugacy-closed not implies weak subset-conjugacy-closed

P-normal not implies p-solvable
type: Subject
page: https://groupprops.subwiki.org/wiki/P-2Dnormal_not_implies_p-2Dsolvable
wiki namespace: 0
wiki page content language: en
wiki page sort key: P-normal not implies p-solvable

Self-normalizing not implies contranormal
type: Subject
page: https://groupprops.subwiki.org/wiki/Self-2Dnormalizing_not_implies_contranormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Self-normalizing not implies contranormal

No nontrivial homomorphism from quotient group not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/No_nontrivial_homomorphism_from_quotient_group_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: No nontrivial homomorphism from quotient group not implies characteristic

Left-transitively WNSCDIN not implies characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Left-2Dtransitively_WNSCDIN_not_implies_characteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Left-transitively WNSCDIN not implies characteristic

Series-equivalent characteristic subgroups may be distinct
type: Subject
page: https://groupprops.subwiki.org/wiki/Series-2Dequivalent_characteristic_subgroups_may_be_distinct
wiki namespace: 0
wiki page content language: en
wiki page sort key: Series-equivalent characteristic subgroups may be distinct

Pure subgroup of torsion-free abelian group not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Pure_subgroup_of_torsion-2Dfree_abelian_group_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Pure subgroup of torsion-free abelian group not implies direct factor

Direct factor not implies amalgam-characteristic
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_factor_not_implies_amalgam-2Dcharacteristic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Direct factor not implies amalgam-characteristic

Abelian-quotient not implies kernel of a bihomomorphism
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian-2Dquotient_not_implies_kernel_of_a_bihomomorphism
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abelian-quotient not implies kernel of a bihomomorphism

Characteristic not implies direct factor
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristic_not_implies_direct_factor
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristic not implies direct factor

Quasiautomorphism-invariant not implies 1-automorphism-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Quasiautomorphism-2Dinvariant_not_implies_1-2Dautomorphism-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Quasiautomorphism-invariant not implies 1-automorphism-invariant

Transitively normal not implies conjugacy-closed normal
type: Subject
page: https://groupprops.subwiki.org/wiki/Transitively_normal_not_implies_conjugacy-2Dclosed_normal
wiki namespace: 0
wiki page content language: en
wiki page sort key: Transitively normal not implies conjugacy-closed normal

Intermediately characteristic not implies isomorph-containing in group of prime power order
type: Subject
page: https://groupprops.subwiki.org/wiki/Intermediately_characteristic_not_implies_isomorph-2Dcontaining_in_group_of_prime_power_order
wiki namespace: 0
wiki page content language: en
wiki page sort key: Intermediately characteristic not implies isomorph-containing in group of prime power order

Complemented normal not implies local powering-invariant
type: Subject
page: https://groupprops.subwiki.org/wiki/Complemented_normal_not_implies_local_powering-2Dinvariant
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complemented normal not implies local powering-invariant

4-subnormal not implies finite-conjugate-join-closed subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/4-2Dsubnormal_not_implies_finite-2Dconjugate-2Djoin-2Dclosed_subnormal
wiki namespace: 0
wiki page content language: en
wiki page sort key: 4-subnormal not implies finite-conjugate-join-closed subnormal

Abelian-quotient not implies cocentral
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian-2Dquotient_not_implies_cocentral
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abelian-quotient not implies cocentral

Modular not implies permutable
type: Subject
page: https://groupprops.subwiki.org/wiki/Modular_not_implies_permutable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Modular not implies permutable

Pronormal not implies join with any distinct conjugate is the whole group
type: Subject
page: https://groupprops.subwiki.org/wiki/Pronormal_not_implies_join_with_any_distinct_conjugate_is_the_whole_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Pronormal not implies join with any distinct conjugate is the whole group

INST
type: DatatypeProperty
page: https://groupprops.subwiki.org/wiki/Property-3A_INST
wiki namespace: 132
wiki page content language: en
wiki page sort key: INST