# Semantic search

Abelian automorphism group implies class two, Center is local powering-invariant, Center of binary von Dyck group has order two, Centerless implies inner automorphism group is centralizer-free in automorphism group, Characteristic implies normal, Cube map is surjective endomorphism implies abelian, Cyclic automorphism group implies abelian, Equivalence of presentations of dicyclic group, Finite and any two maximal subgroups intersect trivially implies not simple non-abelian, Group acts on set of subgroups by conjugation, Left coset space of centralizer is in bijective correspondence with conjugacy class, N-abelian implies every nth power and (n-1)th power commute, Nilpotent automorphism group implies nilpotent of class at most one more, Normality is strongly join-closed, Size of conjugacy class of subgroups equals index of normalizer, Solvable automorphism group implies solvable of derived length at most one more