Quotient-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 quotient-coprime automorphism-faithful if H is a normal subgroup of G, and:

If \varphi is a non-identity automorphism of G whose order is relatively prime to the order of G, such that \varphi(H) = H, then the induced map by \varphi on G/H is also a non-identity automorphism.

Facts

Relation with other properties

Weaker properties