Subnormal automorphism-invariant 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]


A subgroup H of a group G is termed a subnormal automorphism-invariant subgroup if, given any automorphism \varphi of G such that \varphi restricts to an automorphism for every subnormal subgroup of G, \varphi(H) = H.


In terms of the invariance-closure operator

This property is obtained by applying the invariance-closure operator to the property: subnormal subgroup
View other properties obtained by applying the invariance-closure operator

Relation with other properties

Stronger properties