On a conjecture of Kahn for the Stiefel-Whitney classes of the regular representation
type: Item
instance of: scholarly article
title: On a conjecture of Kahn for the Stiefel-Whitney classes of the regular representation
zbMATH Open document ID: 0877.20036
author: Pham Anh Minh
published in: Journal of Algebra
publication date: 1997-12-07T00:00:00Z
review text: Let \(G\) be a finite 2-group and let \(r_G\) denote the regular representation of \(G\). Define \(\nu(G)=\min\{n>0\mid w_{2^{n-1}}(r_G)\neq 0\}\) where \(w_j\) is the \(j^n\)th Stiefel-Whitney class. Let \(d(G)\) denote the minimal number of generators of \(G\). In [\textit{B. Kahn}, J. Algebra 144, No. 1, 214-247 (1991; Zbl 0777.20019)] it was conjectured that \(\nu(G)\geq d(G)\) and proved for \(d(G)\leq 3\). The case when \(d(G)=4\) was proved in [\textit{Pham Anh Minh}, J. Algebra 179, No. 2, 483-500 (1976; Zbl 0855.20043)]. In this paper the authors proves the conjecture when \(d(G)=5\).
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1013940
zbMATH Keywords: finite 2-groups
zbMATH Keywords: regular representations
zbMATH Keywords: Stiefel-Whitney classes
zbMATH Keywords: minimal number of generators
Wikidata QID: Q123157459
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: jabr.1996.6817
OpenAlex ID: W1999615641
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DOI: 10.1006/JABR.1996.6817
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description: scientific article; zbMATH DE number 1013940