The Augmentation Quotients of the Groups of Order 2⁵, I

Abstract

In this article we present the nth power Δ ⁿ (G) of the augmentation ideal Δ(G) and describe the structure of Q _n (G) = Δ ⁿ (G)/Δ ⁿ⁺¹(G) for 35 particular groups G of order 2⁵. The structure of Q _n (G) for all the remaining groups of order 2⁵ will be determined in a forthcoming article.

Key Words:

• Augmentation ideal
• Augmentation quotient group
• Integral group ring

2000 Mathematics Subject Classification:

• 16S34
• 20C05

ACKNOWLEDGMENTS

The authors wish to express their thanks for the referee's prompt and thoughtful reading of this article, and the first author would like to thank the production editor, Kerry Stanley, for understanding and kindness.

Notes

Communicated by S. Sehgal.