Retraction-invariant normal subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: retraction-invariant subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a group is termed a retraction-invariant normal subgroup if it is both a normal subgroup and a retraction-invariant subgroup.

Relation with other properties

Stronger properties

• Fully invariant subgroup
• Retraction-invariant direct factor
• Retraction-invariant central factor
• Retraction-invariant characteristic subgroup

Weaker properties

• Normal subgroup
• Retraction-invariant subgroup