,Uses,"Fact about"
"CDIN of conjugacy-closed implies CDIN",,"Composition operator; ?,CDIN-subgroup; ?,Conjugacy-closed subgroup; ?,Conjugacy-closed subgroup; 2,Right-transitively CDIN-subgroup; 2"
"Conjugacy-closed abelian Sylow implies retract","Focal subgroup theorem","Normal p-complement; ?,P-nilpotent group; ?,Conjugacy-closed subgroup; ?"
"Conjugacy-closed and Hall not implies retract",,"Conjugacy-closed Hall subgroup; 2,Hall retract; 2,Conjugacy-closed subgroup; ?,Retract; ?,Normal Hall subgroup; ?"
"Conjugacy-closed implies focal subgroup equals derived subgroup",,"Conjugacy-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-closed","Brauer'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 ambivalent",,"Conjugacy-closed subgroup; ?,Ambivalent group; ?,Conjugacy-closed normal subgroup; ?,Central factor; ?,Retract; ?,Direct factor; ?"
"Conjugacy-closed subgroup of conjugacy-separable group is conjugacy-separable",,"Conjugacy-separable group; 1,Conjugacy-closed subgroup; 1"
"Conjugacy-closedness is not join-closed",,"Conjugacy-closed subgroup; 1,Join-closed subgroup property; 2"
"Conjugacy-closedness is not upper join-closed",,"Conjugacy-closed subgroup; 1,Upper join-closed subgroup property; 2"
"Conjugacy-closedness is transitive",,"Conjugacy-closed subgroup; 1,Transitive subgroup property; 2"
"Equivalence of definitions of Sylow direct factor","Direct 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 group",,"Alternating group; ?,Conjugacy-closed subgroup; ?,Symmetric group; ?,Conjugacy-closed normal subgroup; ?"
"Finitary symmetric group on subset is conjugacy-closed",,"Conjugacy-closed subgroup; ?,Finitary symmetric group; ?"
"Orthogonal group is conjugacy-closed in general linear group over reals",,"Orthogonal 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-closed",,"Conjugacy-closed subgroup; ?,Symmetric group; ?"
"Symmetric group on infinite coinfinite subset is not conjugacy-closed",,"Conjugacy-closed subgroup; ?,Symmetric group; ?"