Alperin's structure theorem for n-abelian groups

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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


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.