2-2Dsubnormal subgroup
type: Ontology
creation date: 2026-08-31T13:06:52+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

2-subnormal subgroup
type: Subject
type: Category:Semi-basic definitions in group theory
type: Category:Standard terminology
type: Category:Subgroup property compositions
type: Category:Subgroup properties
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_subgroup
wiki namespace: 0
wiki page content language: en
defining ingredient: Normal subgroup
defining ingredient: Conjugate subgroups
defining ingredient: Commutator of two subgroups
defining ingredient: Subnormal subgroup
defining ingredient: Normal closure
defining ingredient: Normalizer of a subgroup
defining ingredient: Subnormal depth
defining ingredient: Normal core of normalizer
defining ingredient: Normal core
definition style: tabular
dissatisfies metaproperty: Transitive subgroup property
dissatisfies metaproperty: Upper join-closed subgroup property
dissatisfies metaproperty: Finite-join-closed subgroup property
page class: Term
satisfies metaproperty: Trim subgroup property
satisfies metaproperty: Strongly intersection-closed subgroup property
satisfies metaproperty: Intermediate subgroup condition
satisfies metaproperty: Transfer condition
satisfies metaproperty: Image condition
satisfies metaproperty: Inverse image condition
satisfies metaproperty: First-order subgroup property
satisfies metaproperty: Conjugate-join-closed subgroup property
stronger than: Subnormal subgroup
stronger than: 3-subnormal subgroup
stronger than: 4-subnormal subgroup
stronger than: Conjugate-permutable subgroup
stronger than: Join of finitely many 2-subnormal subgroups
stronger than: Join of 2-subnormal subgroups
stronger than: Loin-transitively subnormal subgroup
weaker than: Normal subgroup
weaker than: 2-hypernormalized subgroup
weaker than: Direct factor of characteristic subgroup
weaker than: Direct factor of normal subgroup
weaker than: Normal subgroup of characteristic subgroup
weaker than: Base of a wreath product
weaker than: Commutator of a normal subgroup and a subset
wiki page modification date: 2026-08-12T01:43:46Z
modification date#aux: 2461264.5720602
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query depth: 1
query format: broadtable
query size: 4
query string: 4-subnormal subgroup 2-subnormal subgroup
wiki page sort key: 2-subnormal subgroup# QUERY8664c9ebd20dcc429ae36b6b3f0eb469

Commutator of a normal subgroup and a subset implies 2-subnormal
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page: https://groupprops.subwiki.org/wiki/Commutator_of_a_normal_subgroup_and_a_subset_implies_2-2Dsubnormal
wiki namespace: 0
wiki page content language: en
proves property satisfaction of: 2-subnormal subgroup
wiki page sort key: Commutator of a normal subgroup and a subset implies 2-subnormal

2-subnormality is strongly intersection-closed
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormality_is_strongly_intersection-2Dclosed
wiki namespace: 0
wiki page content language: en
proves property satisfaction of: 2-subnormal subgroup
wiki page sort key: 2-subnormality is strongly intersection-closed
uses property satisfaction of: 2-subnormal subgroup

2-subnormal implies conjugate-permutable
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page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_implies_conjugate-2Dpermutable
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: 2-subnormal subgroup
wiki page sort key: 2-subnormal implies conjugate-permutable

2-subnormal implies conjugate-join-closed subnormal
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page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_implies_conjugate-2Djoin-2Dclosed_subnormal
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: 2-subnormal subgroup
wiki page sort key: 2-subnormal implies conjugate-join-closed subnormal

2-subnormal implies join-transitively subnormal
type: Subject
page: https://groupprops.subwiki.org/wiki/2-2Dsubnormal_implies_join-2Dtransitively_subnormal
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: 2-subnormal subgroup
wiki page sort key: 2-subnormal implies join-transitively subnormal

Normal subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Normal_subgroup
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wiki page content language: en
stronger than: 2-subnormal subgroup
wiki page sort key: Normal subgroup

Direct factor of characteristic subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_factor_of_characteristic_subgroup
wiki namespace: 0
wiki page content language: en
stronger than: 2-subnormal subgroup
wiki page sort key: Direct factor of characteristic subgroup

Direct factor of fully invariant subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_factor_of_fully_invariant_subgroup
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wiki page content language: en
stronger than: 2-subnormal subgroup
wiki page sort key: Direct factor of fully invariant subgroup

Subnormal subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Subnormal_subgroup
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wiki page content language: en
weaker than: 2-subnormal subgroup
wiki page sort key: Subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_implies_conjugate-2Dpermutable-23_db64c0f0c5645d44f8272ab0e61431d8
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master page: 2-subnormal implies conjugate-permutable
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wiki page sort key: 2-subnormal implies conjugate-permutable#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Subgroup-2Dcofactorial_automorphism-2Dinvariant_implies_left-2Dtransitively_2-2Dsubnormal-23_41fd7d0391c804842b168579614f366d
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Subgroup-2Dcofactorial_automorphism-2Dinvariant_implies_left-2Dtransitively_2-2Dsubnormal
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wiki page sort key: Subgroup-cofactorial automorphism-invariant implies left-transitively 2-subnormal#2-subnormal subgroup# 41fd7d0391c804842b168579614f366d
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Commutator_of_a_normal_subgroup_and_a_subset_implies_2-2Dsubnormal-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: Commutator of a normal subgroup and a subset implies 2-subnormal
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wiki page sort key: Commutator of a normal subgroup and a subset implies 2-subnormal#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Base_of_a_wreath_product_implies_right-2Dtransitively_2-2Dsubnormal-23_41fd7d0391c804842b168579614f366d
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Base_of_a_wreath_product_implies_right-2Dtransitively_2-2Dsubnormal
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wiki page sort key: Base of a wreath product implies right-transitively 2-subnormal#2-subnormal subgroup# 41fd7d0391c804842b168579614f366d
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Index_four_implies_2-2Dsubnormal_or_double_coset_index_two-23_41fd7d0391c804842b168579614f366d
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master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Index_four_implies_2-2Dsubnormal_or_double_coset_index_two
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wiki page sort key: Index four implies 2-subnormal or double coset index two#2-subnormal subgroup# 41fd7d0391c804842b168579614f366d
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_not_implies_hypernormalized-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_not_implies_hypernormalized
wiki namespace: 0
wiki page sort key: 2-subnormal not implies hypernormalized#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_implies_conjugate-2Djoin-2Dclosed_subnormal-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: 2-subnormal implies conjugate-join-closed subnormal
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wiki page sort key: 2-subnormal implies conjugate-join-closed subnormal#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_not_implies_automorph-2Dpermutable-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_not_implies_automorph-2Dpermutable
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wiki page sort key: 2-subnormal not implies automorph-permutable#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormal_implies_join-2Dtransitively_subnormal-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: 2-subnormal implies join-transitively subnormal
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wiki page sort key: 2-subnormal implies join-transitively subnormal#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

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type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Cofactorial_automorphism-2Dinvariant_implies_left-2Dtransitively_2-2Dsubnormal
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wiki page sort key: Cofactorial automorphism-invariant implies left-transitively 2-subnormal#2-subnormal subgroup# 41fd7d0391c804842b168579614f366d
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Base_of_a_wreath_product_not_implies_elliptic-23_db64c0f0c5645d44f8272ab0e61431d8
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Base_of_a_wreath_product_not_implies_elliptic
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wiki page sort key: Base of a wreath product not implies elliptic#2-subnormal subgroup;2# db64c0f0c5645d44f8272ab0e61431d8
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/3-2Dsubnormal_subgroup_need_not_have_a_unique_fastest_ascending_subnormal_series-23_3e19a6768b399a04ed7957255cf8ee5c
type: Subject
master page: http://groupprops.subwiki.org/wiki/Special:URIResolver/3-2Dsubnormal_subgroup_need_not_have_a_unique_fastest_ascending_subnormal_series
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wiki page sort key: 3-subnormal subgroup need not have a unique fastest ascending subnormal series#2-subnormal subgroup# 3e19a6768b399a04ed7957255cf8ee5c
page: 2-subnormal subgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/2-2Dsubnormality_is_strongly_intersection-2Dclosed-23_2da81e73c9f94b4033f4da9c8aac0f2a
type: Subject
master page: 2-subnormality is strongly intersection-closed
wiki namespace: 0
wiki page sort key: 2-subnormality is strongly intersection-closed#2-subnormal subgroup;1# 2da81e73c9f94b4033f4da9c8aac0f2a
page: 2-subnormal subgroup

Proves property satisfaction of
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wiki namespace: 132
wiki page content language: en
wiki page sort key: Proves property satisfaction of

Uses property satisfaction of
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AUses_property_satisfaction_of
wiki namespace: 132
wiki page content language: en
wiki page sort key: Uses property satisfaction of

Stronger than
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AStronger_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Stronger than

Weaker than
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AWeaker_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Weaker than

Page
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wiki page sort key: Page