Direct factor of fully invariant subgroup

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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 invariant subgroup if it satisfies the following equivalent conditions:

In terms of the composition operator

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

Relation with other properties

Stronger properties

Weaker properties