# Semantic search

Class-preserving automorphism group of finite p-group is p-group, Class-preserving implies IA, Class-preserving implies linearly extensible, Class-preserving implies linearly pushforwardable, Class-preserving not implies inner, Class-preserving not implies subgroup-conjugating, Conjugacy-separable and aperiodic implies every extensible automorphism is class-preserving, Conjugacy-separable implies every quotient-pullbackable automorphism is class-preserving, Conjugacy-separable with only finitely many prime divisors of orders of elements implies every extensible automorphism is class-preserving, Finite solvable-extensible implies class-preserving, Finite-extensible implies class-preserving, Finite-quotient-pullbackable implies class-preserving, Hall-extensible implies class-preserving, IA not implies class-preserving, Inner implies class-preserving, Linearly pushforwardable implies class-preserving for class-separating field, Preserves conjugacy classes for a generating set not implies class-preserving, Subgroup-conjugating not implies class-preserving