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 UsesFact about
CDIN of conjugacy-closed implies CDINComposition operator (?)
CDIN-subgroup (?)
Conjugacy-closed subgroup (?)
Conjugacy-closed subgroup (2)
Right-transitively CDIN-subgroup (2)
Conjugacy-closed abelian Sylow implies retractFocal subgroup theoremNormal p-complement (?)
P-nilpotent group (?)
Conjugacy-closed subgroup (?)
Conjugacy-closed and Hall not implies retractConjugacy-closed Hall subgroup (2)
Hall retract (2)
Conjugacy-closed subgroup (?)
Retract (?)
Normal Hall subgroup (?)
Conjugacy-closed implies focal subgroup equals derived subgroupConjugacy-closed subgroup (2)
Subgroup whose focal subgroup equals its derived subgroup (2)
Focal subgroup of a subgroup (?)
Derived subgroup (?)
Conjugacy-closed not implies weak subset-conjugacy-closedBrauer's permutation lemma
Symmetric group of degree six or higher is not weak subset-conjugacy-closed in general linear group over rationals
Conjugacy-closed subgroup (2)
Weak subset-conjugacy-closed subgroup (2)
Subset-conjugacy-closed subgroup (?)
Conjugacy-closed subgroup of ambivalent group is ambivalentConjugacy-closed subgroup (?)
Ambivalent group (?)
Conjugacy-closed normal subgroup (?)
Central factor (?)
Retract (?)
Direct factor (?)
Conjugacy-closed subgroup of conjugacy-separable group is conjugacy-separableConjugacy-separable group (1)
Conjugacy-closed subgroup (1)
Conjugacy-closedness is not join-closedConjugacy-closed subgroup (1)
Join-closed subgroup property (2)
Conjugacy-closedness is not upper join-closedConjugacy-closed subgroup (1)
Upper join-closed subgroup property (2)
Conjugacy-closedness is transitiveConjugacy-closed subgroup (1)
Transitive subgroup property (2)
Equivalence of definitions of Sylow direct factorDirect factor implies central factor
Central factor implies conjugacy-closed normal
Class-preserving automorphism group of finite p-group is p-group
Hall and central factor implies direct factor
Sylow direct factor (1)
Conjugacy-closed subgroup (?)
Finitary alternating group is conjugacy-closed in symmetric groupAlternating group (?)
Conjugacy-closed subgroup (?)
Symmetric group (?)
Conjugacy-closed normal subgroup (?)
Finitary symmetric group on subset is conjugacy-closedConjugacy-closed subgroup (?)
Finitary symmetric group (?)
Orthogonal group is conjugacy-closed in general linear group over realsOrthogonal group over reals (?)
Conjugacy-closed subgroup (?)
General linear group over reals (?)
Special orthogonal group over reals (?)
Symmetric group on finite or cofinite subset is conjugacy-closedConjugacy-closed subgroup (?)
Symmetric group (?)
Symmetric group on infinite coinfinite subset is not conjugacy-closedConjugacy-closed subgroup (?)
Symmetric group (?)