A remark on the Loewy-layers of the modular group algebra of a finite p- group
type: Item
instance of: scholarly article
title: A remark on the Loewy-layers of the modular group algebra of a finite p- group
zbMATH Open document ID: 0607.20004
DOI: 10.1016/0166-8641(87)90004-6
author: Urs Stammbach
author: M. Stricker
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let G be a group of order \(p^ n\) and class n-1, and let J be the augmentation ideal of KG, where K is a field of characteristic p. For \(r\geq 0\), let \(c_ r\) be the dimension of \(J^ r/J^{r+1}\) over K. The dimension of \(\kappa_ nG/\kappa_{n+1}G\) is easily found from the structure of G, and a formula of Jennings then enables the \(c_ r\) to be calculated. This is used to show by hand that if \(p^ n=3^ 5\), then \(c_{10}\geq c_{11}\leq c_{12}\geq c_{13}\), and by computer that if \(p^ n=5^ 7\), \(c_{50}\geq c_{51}\leq c_{52}\). Using a theorem of Quillen, it is shown that the Lie algebras of these groups have the corresponding property.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F40
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 3981412
zbMATH Keywords: p-groups
zbMATH Keywords: powers of augmentation ideal
zbMATH Keywords: dimension
reviewed by: Norman Blackburn
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90004-6
OpenAlex ID: W2065903518
cites work: On a special class of \(p\)-groups
cites work: Q3934684
cites work: The Structure of the Group Ring of a p-Group Over a Modular Field
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description: scientific article; zbMATH DE number 3981412