Finite group whose outer automorphism group is cyclic
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finite group and group whose outer automorphism group is cyclic
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Definition
A finite group whose outer automorphism group is cyclic is a finite group that is also a group whose outer automorphism group is cyclic, i.e., the outer automorphism group is a cyclic group (and in particular a finite cyclic group).
Relation with other properties
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Finite group with cyclic quotient of automorphism group by class-preserving automorphism group | ||||
| Finite group whose automorphism group has equivalent actions on the sets of conjugacy classes and irreducible representations | ||||
| Finite group having the same orbit sizes of conjugacy classes and irreducible representations under automorphism group |