The Coexponent of a Regular p-Group

Abstract

A sharp bound is derived for the nilpotency class of a regular p-group in terms of its coexponent, and is used to show that the number of groups of order p^n with a given fixed coexponent, is independent of n, for p and n sufficiently large. Explicit formulae are calculated in the case of coexponent 3.

arXiv comment23 pages. In LaTeX2e using packages amsmath, amssymb and enumerate. Submitted for publication in Comm. Algebra