Alperin's structure theorem for n-abelian groups

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.