https://groupprops.subwiki.org/wiki/Special:ExportRDF/Category-3AGroup_property_non-2Dimplications
type: Ontology
creation date: 2026-03-11T03:52:57+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Group property non-implications
type: Class
page: https://groupprops.subwiki.org/wiki/Category-3AGroup_property_non-2Dimplications
wiki namespace: 14
wiki page content language: en
wiki page sort key: Group property non-implications

Cyclic automorphism group not implies cyclic
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_automorphism_group_not_implies_cyclic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Cyclic automorphism group not implies cyclic

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

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

Complete not implies ambivalent
type: Subject
page: https://groupprops.subwiki.org/wiki/Complete_not_implies_ambivalent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Complete not implies ambivalent

Glauberman type not implies p-constrained
type: Subject
page: https://groupprops.subwiki.org/wiki/Glauberman_type_not_implies_p-2Dconstrained
wiki namespace: 0
wiki page content language: en
wiki page sort key: Glauberman type not implies p-constrained

Locally finite not implies embeddable in finitary symmetric group
type: Subject
page: https://groupprops.subwiki.org/wiki/Locally_finite_not_implies_embeddable_in_finitary_symmetric_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally finite not implies embeddable in finitary symmetric group

Abelian automorphism group not implies abelian
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian_automorphism_group_not_implies_abelian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abelian automorphism group not implies abelian

Finitely generated and parafree not implies free
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_and_parafree_not_implies_free
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated and parafree not implies free

Isomorphic to inner automorphism group not implies centerless
type: Subject
page: https://groupprops.subwiki.org/wiki/Isomorphic_to_inner_automorphism_group_not_implies_centerless
wiki namespace: 0
wiki page content language: en
wiki page sort key: Isomorphic to inner automorphism group not implies centerless

Characteristically metacyclic not implies metacyclic derived series
type: Subject
page: https://groupprops.subwiki.org/wiki/Characteristically_metacyclic_not_implies_metacyclic_derived_series
wiki namespace: 0
wiki page content language: en
wiki page sort key: Characteristically metacyclic not implies metacyclic derived series

P-group not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/P-2Dgroup_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: P-group not implies nilpotent

Locally free not implies free
type: Subject
page: https://groupprops.subwiki.org/wiki/Locally_free_not_implies_free
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally free not implies free

P-constrained not implies Glauberman type for p
type: Subject
page: https://groupprops.subwiki.org/wiki/P-2Dconstrained_not_implies_Glauberman_type_for_p
wiki namespace: 0
wiki page content language: en
wiki page sort key: P-constrained not implies Glauberman type for p

Subgroups of all orders dividing the group order not implies supersolvable
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroups_of_all_orders_dividing_the_group_order_not_implies_supersolvable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subgroups of all orders dividing the group order not implies supersolvable

Nilpotent not implies nilpotent automorphism group
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_not_implies_nilpotent_automorphism_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nilpotent not implies nilpotent automorphism group

Torsion-free not implies powering-injective
type: Subject
page: https://groupprops.subwiki.org/wiki/Torsion-2Dfree_not_implies_powering-2Dinjective
wiki namespace: 0
wiki page content language: en
wiki page sort key: Torsion-free not implies powering-injective

Noetherian not implies finitely presented
type: Subject
page: https://groupprops.subwiki.org/wiki/Noetherian_not_implies_finitely_presented
wiki namespace: 0
wiki page content language: en
wiki page sort key: Noetherian not implies finitely presented

Finitely generated not implies Noetherian
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_not_implies_Noetherian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated not implies Noetherian

FC not implies finite derived subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/FC_not_implies_finite_derived_subgroup
wiki namespace: 0
wiki page content language: en
wiki page sort key: FC not implies finite derived subgroup

Perfect not implies semisimple
type: Subject
page: https://groupprops.subwiki.org/wiki/Perfect_not_implies_semisimple
wiki namespace: 0
wiki page content language: en
wiki page sort key: Perfect not implies semisimple

Golod's theorem on locally finite groups
type: Subject
page: https://groupprops.subwiki.org/wiki/Golod-27s_theorem_on_locally_finite_groups
wiki namespace: 0
wiki page content language: en
wiki page sort key: Golod's theorem on locally finite groups

Finitely presented and solvable not implies polycyclic
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_presented_and_solvable_not_implies_polycyclic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely presented and solvable not implies polycyclic

Ambivalent not implies strongly ambivalent
type: Subject
page: https://groupprops.subwiki.org/wiki/Ambivalent_not_implies_strongly_ambivalent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Ambivalent not implies strongly ambivalent

Solvable and generated by finitely many periodic elements not implies periodic
type: Subject
page: https://groupprops.subwiki.org/wiki/Solvable_and_generated_by_finitely_many_periodic_elements_not_implies_periodic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Solvable and generated by finitely many periodic elements not implies periodic

Finitely generated and solvable not implies finitely presented
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_and_solvable_not_implies_finitely_presented
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated and solvable not implies finitely presented

Finitely generated not implies finitely presented
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_not_implies_finitely_presented
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated not implies finitely presented

Nilpotent automorphism group not implies abelian automorphism group
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_automorphism_group_not_implies_abelian_automorphism_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nilpotent automorphism group not implies abelian automorphism group

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

2-Engel not implies class two for groups
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2DEngel_not_implies_class_two_for_groups
wiki namespace: 0
wiki page content language: en
wiki page sort key: 2-Engel not implies class two for groups

CA not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/CA_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: CA not implies nilpotent

Finitely presented not implies Noetherian
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_presented_not_implies_Noetherian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely presented not implies Noetherian

Sylow tower not implies subgroups of all orders dividing the group order
type: Subject
page: https://groupprops.subwiki.org/wiki/Sylow_tower_not_implies_subgroups_of_all_orders_dividing_the_group_order
wiki namespace: 0
wiki page content language: en
wiki page sort key: Sylow tower not implies subgroups of all orders dividing the group order

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

Rational not implies rational-representation
type: Subject
page: https://groupprops.subwiki.org/wiki/Rational_not_implies_rational-2Drepresentation
wiki namespace: 0
wiki page content language: en
wiki page sort key: Rational not implies rational-representation

Solvable not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/Solvable_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Solvable not implies nilpotent

Finite derived subgroup not implies FZ
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_derived_subgroup_not_implies_FZ
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite derived subgroup not implies FZ

Virtually abelian not implies FZ
type: Subject
page: https://groupprops.subwiki.org/wiki/Virtually_abelian_not_implies_FZ
wiki namespace: 0
wiki page content language: en
wiki page sort key: Virtually abelian not implies FZ

Locally nilpotent not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/Locally_nilpotent_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally nilpotent not implies nilpotent

There exist abelian groups whose isomorphism classes of direct powers have any given period
type: Subject
page: https://groupprops.subwiki.org/wiki/There_exist_abelian_groups_whose_isomorphism_classes_of_direct_powers_have_any_given_period
wiki namespace: 0
wiki page content language: en
wiki page sort key: There exist abelian groups whose isomorphism classes of direct powers have any given period

Subgroups of all orders dividing the group order not implies Sylow tower
type: Subject
page: https://groupprops.subwiki.org/wiki/Subgroups_of_all_orders_dividing_the_group_order_not_implies_Sylow_tower
wiki namespace: 0
wiki page content language: en
wiki page sort key: Subgroups of all orders dividing the group order not implies Sylow tower

Same Hall-Senior genus not implies character table-equivalent
type: Subject
page: https://groupprops.subwiki.org/wiki/Same_Hall-2DSenior_genus_not_implies_character_table-2Dequivalent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Same Hall-Senior genus not implies character table-equivalent

Finite solvable not implies supersolvable
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_solvable_not_implies_supersolvable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite solvable not implies supersolvable

Locally nilpotent not implies normalizer condition
type: Subject
page: https://groupprops.subwiki.org/wiki/Locally_nilpotent_not_implies_normalizer_condition
wiki namespace: 0
wiki page content language: en
wiki page sort key: Locally nilpotent not implies normalizer condition

Solvable not implies solvable automorphism group
type: Subject
page: https://groupprops.subwiki.org/wiki/Solvable_not_implies_solvable_automorphism_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Solvable not implies solvable automorphism group

Dedekind not implies abelian
type: Subject
page: https://groupprops.subwiki.org/wiki/Dedekind_not_implies_abelian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Dedekind not implies abelian

Finite solvable not implies subgroups of all orders dividing the group order
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_solvable_not_implies_subgroups_of_all_orders_dividing_the_group_order
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite solvable not implies subgroups of all orders dividing the group order

Supersolvable not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/Supersolvable_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Supersolvable not implies nilpotent

Class two not implies abelian automorphism group
type: Subject
page: https://groupprops.subwiki.org/wiki/Class_two_not_implies_abelian_automorphism_group
wiki namespace: 0
wiki page content language: en
wiki page sort key: Class two not implies abelian automorphism group

Residually finite not implies Hopfian
type: Subject
page: https://groupprops.subwiki.org/wiki/Residually_finite_not_implies_Hopfian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Residually finite not implies Hopfian

Imperfect not implies hypoabelian
type: Subject
page: https://groupprops.subwiki.org/wiki/Imperfect_not_implies_hypoabelian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Imperfect not implies hypoabelian

Finitely generated and solvable not implies polycyclic
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_and_solvable_not_implies_polycyclic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated and solvable not implies polycyclic

Nilpotent not implies UL-equivalent
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_not_implies_UL-2Dequivalent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nilpotent not implies UL-equivalent

Abelian automorphism group not implies cyclic
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian_automorphism_group_not_implies_cyclic
wiki namespace: 0
wiki page content language: en
wiki page sort key: Abelian automorphism group not implies cyclic

Hypoabelian not implies imperfect
type: Subject
page: https://groupprops.subwiki.org/wiki/Hypoabelian_not_implies_imperfect
wiki namespace: 0
wiki page content language: en
wiki page sort key: Hypoabelian not implies imperfect

Rationally powered not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/Rationally_powered_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Rationally powered not implies nilpotent

Finite not implies composition factor-unique
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_not_implies_composition_factor-2Dunique
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite not implies composition factor-unique

Composition factor-unique not implies composition series-unique
type: Subject
page: https://groupprops.subwiki.org/wiki/Composition_factor-2Dunique_not_implies_composition_series-2Dunique
wiki namespace: 0
wiki page content language: en
wiki page sort key: Composition factor-unique not implies composition series-unique

No proper nontrivial transitively normal subgroup not implies simple
type: Subject
page: https://groupprops.subwiki.org/wiki/No_proper_nontrivial_transitively_normal_subgroup_not_implies_simple
wiki namespace: 0
wiki page content language: en
wiki page sort key: No proper nontrivial transitively normal subgroup not implies simple

Residually finite not implies finitely generated
type: Subject
page: https://groupprops.subwiki.org/wiki/Residually_finite_not_implies_finitely_generated
wiki namespace: 0
wiki page content language: en
wiki page sort key: Residually finite not implies finitely generated

Residually nilpotent not implies imperfect
type: Subject
page: https://groupprops.subwiki.org/wiki/Residually_nilpotent_not_implies_imperfect
wiki namespace: 0
wiki page content language: en
wiki page sort key: Residually nilpotent not implies imperfect

Divisible not implies rationally powered
type: Subject
page: https://groupprops.subwiki.org/wiki/Divisible_not_implies_rationally_powered
wiki namespace: 0
wiki page content language: en
wiki page sort key: Divisible not implies rationally powered

Nilpotent not implies generated by abelian normal subgroups
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_not_implies_generated_by_abelian_normal_subgroups
wiki namespace: 0
wiki page content language: en
wiki page sort key: Nilpotent not implies generated by abelian normal subgroups

Finitely generated not implies residually finite
type: Subject
page: https://groupprops.subwiki.org/wiki/Finitely_generated_not_implies_residually_finite
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finitely generated not implies residually finite

FC not implies BFC
type: Subject
page: https://groupprops.subwiki.org/wiki/FC_not_implies_BFC
wiki namespace: 0
wiki page content language: en
wiki page sort key: FC not implies BFC

Simple not implies co-Hopfian
type: Subject
page: https://groupprops.subwiki.org/wiki/Simple_not_implies_co-2DHopfian
wiki namespace: 0
wiki page content language: en
wiki page sort key: Simple not implies co-Hopfian

Normalizer condition not implies nilpotent
type: Subject
page: https://groupprops.subwiki.org/wiki/Normalizer_condition_not_implies_nilpotent
wiki namespace: 0
wiki page content language: en
wiki page sort key: Normalizer condition not implies nilpotent

Finite not implies composition factor-permutable
type: Subject
page: https://groupprops.subwiki.org/wiki/Finite_not_implies_composition_factor-2Dpermutable
wiki namespace: 0
wiki page content language: en
wiki page sort key: Finite not implies composition factor-permutable

Periodic not implies locally finite
type: Subject
page: https://groupprops.subwiki.org/wiki/Periodic_not_implies_locally_finite
wiki namespace: 0
wiki page content language: en
wiki page sort key: Periodic not implies locally finite

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