Groups with isomorphic Burnside rings
type: Item
instance of: scholarly article
title: Groups with isomorphic Burnside rings
zbMATH Open document ID: 1068.19003
author: Luis Valero-Elizondo
author: Alberto G. Raggi-Cárdenas
published in: Archiv der Mathematik
publication date: 2005-04-28T00:00:00Z
review text: Let \(G\) be a finite group and \(B(G)\) denote its Burnside ring. One may ask when \(B(G)\) determines the isomorphism class of \(G\). The authors prove that this is the case in the following cases: Let \(G\) and \(G'\) be finite groups with isomorphic Burnside rings then \(G\) is isomorphic to \(G'\) if (Theorem 3.1): \(G\) is Hamiltonian or abelian, or (Theorem 4.1): both \(G\) and \(G'\) are simple, or (Theorem 4.2): \(G\) is minimal simple, where \(G\) is minimal simple if \(G\) is simple non-abelian and its proper subgroups are solvable. These results are based on a previous work by the authors [\textit{A. G. Raggi-Cárdenas} and \textit{L. Valero-Elizondo}, ``Normalizing isomorphisms between Burnside rings'', J. Algebra 277, 643--657 (2004; Zbl 1055.19001)], where they explore more profoundly the consequences on finite groups \(G\) and \(G'\) with isomorphic Burnside rings.
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 2162321
zbMATH Keywords: Burnside rings
reviewed by: Daniel Juan Pineda
MaRDI profile type: Publication
full work available at URL: s00013-004-1124-x
OpenAlex ID: W2397589654
DOI: 10.1007/S00013-004-1124-X
description: scientific article; zbMATH DE number 2162321