Automorphism-faithful subgroup

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]


Symbol-free definition

A subgroup of a group is termed automorphism-faithful if any nontrivial automorphism of the whole group that restricts to an automorphism of the subgroup, in fact restricts to a nontriival automorphism of the subgroup.

Definition with symbols

A subgroup H of a group G is termed automorphism-faithful in G if for any nontrivial automorphism \sigma of G such that \sigma(H) = H, the restriction of \sigma to H is a nontrivial automorphism of H.

Relation with other properties

Stronger properties

Weaker properties