# Hereditarily 2-subnormal subgroup

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Contents

## Definition

### Definition with symbols

A subgroup of a group is termed a **hereditarily 2-subnormal subgroup** if, for any subgroup of , is a 2-subnormal subgroup of .

## Formalisms

### In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: 2-subnormal subgroup

View other properties obtained by applying the hereditarily operator

## Relation with other properties

### Stronger properties

- Central subgroup
- Abelian normal subgroup
- Subgroup of abelian normal subgroup
- Dedekind normal subgroup
- Subgroup of Dedekind normal subgroup
- Subgroup contained in the Baer norm