\(G\)-algebras, Clifford theory, and the Green correspondence
type: Item
instance of: scholarly article
title: \(G\)-algebras, Clifford theory, and the Green correspondence
zbMATH Open document ID: 0835.20013
DOI: 10.1016/S0021-8693(05)80006-7
author: Laurence Barker
published in: Journal of Algebra
publication date: 1996-04-11T00:00:00Z
review text: Let \(p\) be a prime, let \(\mathcal O\) be a suitable \(p\)-adic ring, and let \(H\) be a subgroup of a finite group \(G\). Moreover, let \(A\) be a \(G\)-algebra, let \(\alpha\), \(\beta\) be points of \(G\) and \(H\), respectively, on \(A\), and suppose that \(G_\alpha\) and \(H_\beta\) have a common defect pointed subgroup \(P_\gamma\) such that \(N_G(P_\gamma)\leq H\). The author shows that \(H_\beta \leq G_\alpha\) if and only if \(\alpha\subseteq\text{Tr}^G_H(A^H\beta A^H)\). Then he looks at this situation in more detail. Fixing \(\beta\), he studies the possible \(\alpha\), and conversely. He also indicates how his results apply to Clifford theory, the Green correspondence, the Burry-Carlson-Puig theorem and Brauer's (extended) first main theorem.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 763197
zbMATH Keywords: finite groups
zbMATH Keywords: \(G\)-algebras
zbMATH Keywords: defect pointed subgroups
zbMATH Keywords: Clifford theory
zbMATH Keywords: Green correspondence
zbMATH Keywords: Burry-Carlson-Puig theorem
zbMATH Keywords: Brauer's (extended) first main theorem
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
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full work available at URL: s0021-8693(05)80006-7
OpenAlex ID: W2023097369
description: scientific article; zbMATH DE number 763197