Direct factor of fully characteristic subgroup

From Groupprops
Jump to: navigation, search
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: direct factor and fully characteristic subgroup
View other such compositions|View all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a direct factor of fully characteristic subgroup if it satisfies the following equivalent conditions:

In terms of the composition operator

The subgroup property of being a DFFC-subgroup is obtained by applying the composition operator to the subgroup properties of being a direct factor and of being fully characteristic.

Relation with other properties

Stronger properties

Weaker properties