Stable augmentation quotients of abelian groups

Alfred Washington Hales

Vol. 118 (1985), No. 2, 401–410

DOI: 10.2140/pjm.1985.118.401

Abstract

Let G be a finite abelian p-group, ZG the associated integral group ring, and Δ its augmentation ideal. This paper determines the stable structure of the augmentation quotients Δⁿ∕Δⁿ⁺¹ and the structure of the graded ring gr ZG. It also gives an application to the dimension subgroup problem, extending earlier results of Gupta-Hales-Passi.

Mathematical Subject Classification 2000

Primary: 20C05

Milestones

Received: 22 October 1984

Published: 1 June 1985