Calculating Clifford classes for characters containing a linear character once.
type: Item
instance of: scholarly article
title: Calculating Clifford classes for characters containing a linear character once.
zbMATH Open document ID: 1035.20007
DOI: 10.1016/S0021-8693(02)00089-3
author: Alexandre Turull
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: Because of the details, spread out over the paper, the contents of the paper is difficult to expose in a short review. Let us confine ourselves to the following remarks. In previous papers, the author wrote about equivalence of \(G\)-classes [see J. Pure Appl. Algebra 98, No. 2, 209-222 (1995; Zbl 0833.20012) and Commun. Algebra 22, No. 12, 5037-5078 (1994; Zbl 0810.20008) and Proc. Am. Math. Soc. 123, No. 6, 1655-1660 (1995; Zbl 0841.20013)], on Clifford theory for cyclic quotient groups [J. Algebra 227, No. 1, 133-158 (2000; Zbl 0959.20010)] and on a formula for calculating some Schur indices [J. Algebra 227, No. 1, 124-132 (2000; Zbl 0976.20009)]. Here, he pursues these matters further. To be specific about the paper under review: Given a finite group \(G\), a normal subgroup \(N\) of \(G\) and \(\chi\in\text{Irr}(G)\), the Clifford class of \(\chi\) describes the Clifford theory including Schur indices of \(\chi\) with respect to \(N\). Assume there exists a subgroup \(U\) of \(N\) and a linear character \(\vartheta\) of \(U\) with \((\chi_N,\vartheta)=1\). Here, a method is described to calculate the Clifford class of \(\chi\) in certain cases. This method helps, for instance, in the calculation of the Schur indices of the irreducible characters of the groups contained between the general linear groups and the special linear groups.
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1867980
zbMATH Keywords: Clifford theory
zbMATH Keywords: Schur indices
zbMATH Keywords: Clifford classes
zbMATH Keywords: Brauer-Wall groups
zbMATH Keywords: \(G\)-algebras
zbMATH Keywords: Galois groups
zbMATH Keywords: 2-cocycles
zbMATH Keywords: irreducible characters
zbMATH Keywords: general linear groups
zbMATH Keywords: special linear groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
cites work: Q3961610
cites work: Clifford theory with Schur indices
cites work: Some invariants for equivalent \(G\)-algebras
cites work: Equivalence of g-algebras with complemented centroid
cites work: Equivalence of G-Algebras for Abelian G
cites work: Clifford theory for cyclic quotient groups
cites work: A formula for calculating some Schur indices
description: scientific article; zbMATH DE number 1867980