Group in which every automorphism is class-preserving
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
A group is termed a group in which every automorphism is class-preserving if it satisfies the following equivalent conditions:
- Every automorphism of the group is a class-preserving automorphism, i.e., it sends each element to within its conjugacy class.
- Every element of the group is automorph-conjugate, i.e., if two elements of the group are related by an automorphism, then they are in fact conjugate elements, i.e., they are in the same conjugacy class.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|complete group||Group in which every automorphism is inner|FULL LIST, MORE INFO|
|group in which every automorphism is inner|||FULL LIST, MORE INFO|