Jennings' theorem for \(p\)-split groups.
type: Item
instance of: scholarly article
title: Jennings' theorem for \(p\)-split groups.
zbMATH Open document ID: 1090.20002
author: Darren Semmen
published in: Journal of Algebra
publication date: 2005-04-18T00:00:00Z
review text: \textit{S.~A.~Jennings} gave a description [Trans. Am. Math. Soc. 50, 175--185 (1941; Zbl 0025.24401)] of bases of the radical layers of the group ring of a finite \(p\)-group \(G\) over a field of characteristic \(p\), in terms of the descending central series of \(G\) given by the dimension subgroups. \textit{J.~L.~Alperin} later extended this [Q. J. Math., Oxf. (2) 39, 129--133 (1988; Zbl 0657.20004)] to permutation modules for finite \(p\)-groups. The goal of the paper under review is to give a natural extension of these results, covering also associated Hilbert polynomials, to \(p\)-split groups, that is, to those finite groups which have a normal \(p\)-Sylow subgroup.
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 2157757
zbMATH Keywords: Jennings series
zbMATH Keywords: dimension subgroups
zbMATH Keywords: \(p\)-split groups
zbMATH Keywords: Hilbert polynomials
zbMATH Keywords: group rings
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.033
OpenAlex ID: W1972930285
cites work: LOEWY STRUCTURE OF PERMUTATION MODULES FOR p-GROUPS
cites work: Projective Modules, Filtrations and Cartan Invariants
cites work: Q4399851
cites work: The Annihilator of Radical Powers in the Modular Group Ring of A p-Group
cites work: Q4692797
cites work: Q3934684
cites work: The Structure of the Group Ring of a p-Group Over a Modular Field
cites work: Sur les groupes nilpotents et les anneaux de Lie
cites work: On the associated graded ring of a group ring
cites work: Q3856855
cites work: Graded Permutation Modules and a Theorem of Quillen
DOI: 10.1016/J.JALGEBRA.2004.08.033
description: scientific article; zbMATH DE number 2157757