The Coexponent of a Regular p-Group

1998/11/01 by Paul J. Sanders, Sanders, Paul J.
Mathematics · #20D15 #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Rings, Modules, and Algebras #math.GR #msc:20D15

paper · pdf · doi:10.48550/arxiv.math/9811004

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

arxiv created 1998/11/01 · openalex publication_date 1998/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 pⁿ 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.

Citations

• On a special class of p-groups

Related

• A Bound for the Nilpotency Class of a Finite p-Group in terms of its Coexponent
• A note on the bound for the class of certain nilpotent groups
• Finite p-Groups of Nilpotency Class 3 with Two Conjugacy Class Sizes
• p-groups with exactly four codegrees
• A Sufficient Condition for Nilpotency in a Finite Group