Coprime automorphism-faithful subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of a finite group G is termed coprime automorphism-faithful if, given any non-identity automorphism \sigma \in \operatorname{Aut}(G) such that \sigma(H) = H, and such that the order of \sigma is relatively prime to the order of G, \sigma acts nontrivially on H. Equivalently, any coprime automorphism group of G that acts trivially on G must be trivial.

Relation with other properties