# Alperin's structure theorem for n-abelian groups

From Groupprops

This article gives a proof/explanation of the equivalence of multiple definitions for the term n-abelian group

View a complete list of pages giving proofs of equivalence of definitions

## Statement

Suppose is a group and is an integer other than 0 or 1. The following are equivalent:

- is a n-abelian group.
- is isomorphic to a subquotient of a group that is the external direct product of a group of exponent dividing , a group of exponent dividing , and an abelian group.