# Subgroup of finite abelian group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on theambient group: finite abelian group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A **subgroup of finite abelian group** is a subgroup of a finite abelian group.

## Relation with other properties

### Stronger properties

### Weaker properties

- Normal subgroup of finite group
- Subgroup of finite nilpotent group
- Subnormal subgroup of finite group
- Subgroup whose index of intersection with any subgroup divides the index of that subgroup
- Subgroup of finite solvable group
- Subgroup whose composition factors are a subset of the composition factors of the whole group