# Semantic search

Centerless and characteristic in automorphism group implies automorphism group is complete, Characteristically simple and non-abelian implies automorphism group is complete, Complete and composition factor-equivalent not implies isomorphic, Complete not implies ambivalent, Every finite group is the Fitting quotient of a p-dominated group for any prime p not dividing its order, Every group is a malnormal subgroup of a complete group, Holomorph of cyclic group of odd prime order is complete, Holomorph of elementary abelian group not implies every automorphism is inner, Projective general linear group of degree two over a prime field is complete, Semidirect product with self-normalizing subgroup of automorphism group of coprime order implies every automorphism is inner, Symmetric groups on finite sets are complete