Group in which every 1-automorphism is automorphism class-preserving

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group in which every 1-automorphism is automorphism class-preserving is a group with the property that any 1-automorphism of the group (i.e., any bijection that restricts to isomorphisms on cyclic subgroups) sends every element to an element that is in the same orbit under the action of the automorphism group, i.e., every element is sent within its automorphism class.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite abelian group