# Complemented transitively normal subgroup

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutably complemented subgroup and transitively normal subgroup

View other subgroup property conjunctions | view all subgroup properties

## Definition

### Symbol-free definition

A subgroup of a group is termed a **complemented transitively normal subgroup** if it satisfies the following equivalent conditions:

- It is a permutably complemented subgroup as well as a transitively normal subgroup.
- It is a complemented normal subgroup as well as a transitively normal subgroup.