# Group in which every cyclic subgroup is 2-subnormal

From Groupprops

## Contents

## Definition

### Symbol-free definition

A **group in which every cyclic subgroup is 2-subnormal** is a group with the property that every cyclic subgroup (i.e., the subgroup generated by any subset of the group) of the group is a 2-subnormal subgroup.

## Formalisms

### In terms of the subgroup property collapse operator

This group property can be defined in terms of the collapse of two subgroup properties. In other words, a group satisfies this group property if and only if every subgroup of it satisfying the first property (cyclic subgroup) satisfies the second property (cyclic 2-subnormal subgroup), and vice versa.

View other group properties obtained in this way

## Relation with other properties

### Stronger properties

- Abelian group
- Dedekind group
- Group of nilpotence class two
- Group in which every subgroup is 2-subnormal