Coprime automorphism-faithful characteristic subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and coprime automorphism-faithful subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup H of a finite group G is termed copime automorphism-faithful characteristic if every automorphism of G restricts to an automorphism of H (i.e., H is a characteristic subgroup) and if K is the kernel of the map:

\operatorname{Aut}(G) \to \operatorname{Aut}(H)

defined by restriction, then every prime divisor of the order of K, divides the order of G.

Relation with other properties

Stronger properties

Weaker properties