Normal subgroup of complemented normal subgroup

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: normal subgroup and complemented normal subgroup
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Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a normal subgroup of complemented normal subgroup if there exists a subgroup $K$ of $G$ containing $H$ such that $H$ is a normal subgroup 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
• Direct factor of complemented normal subgroup
• Complemented normal subgroup of complemented normal subgroup

Weaker properties

• 2-subnormal subgroup