# Semantic search

Abelian permutable complement to core-free subgroup is-self-centralizing, Central product decomposition lemma for characteristic rank one, Diagonal subgroup is self-centralizing in general linear group, Maximal among abelian normal implies self-centralizing in nilpotent, Maximal among abelian normal implies self-centralizing in supersolvable, Pi-separable and pi'-core-free implies pi-core is self-centralizing, Solvable implies Fitting subgroup is self-centralizing, Thompson's critical subgroup theorem