Direct factor of complemented normal subgroup

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: direct factor and complemented normal subgroup
View other such compositions|View all subgroup properties

Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a direct factor of complemented normal subgroup if there exists an intermediate subgroup $K$ of $G$ containing $H$ such that $H$ is a direct factor of $K$ and $K$ is a complemented normal subgroup of $G$.

Relation with other properties

Stronger properties

• Base of a wreath product
• Base of a wreath product with diagonal action

Weaker properties

• Complemented normal subgroup of complemented normal subgroup
• Direct factor of normal subgroup
• Normal subgroup of complemented normal subgroup
• Complemented normal subgroup of normal subgroup
• 2-subnormal subgroup