Alperin's structure theorem for n-abelian groups

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

1. $G$ is a n-abelian group.
2. $G$ is isomorphic to a subquotient of a group that is the external direct product of a group of exponent dividing $n$, a group of exponent dividing $n-1$, and an abelian group.