Open main menu

Groupprops β

Finite group with cyclic quotient of automorphism group by class-preserving automorphism group

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finite group and group with cyclic quotient of automorphism group by class-preserving automorphism group
View other group property conjunctions OR view all group properties

Contents

Definition

A finite group with cyclic quotient of automorphism group by class-preserving automorphism group is a finite group that is also a group with cyclic quotient of automorphism group by class-preserving automorphism group, i.e., a group such that the quotient group of its automorphism group by the normal subgroup comprising the class-preserving automorphisms is a cyclic group (and in particular, a finite cyclic group).

Relation with other properties