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Computing characters of groups with central subgroups

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 November 2013

Vahid Dabbaghian  and
John D. Dixon
Vahid Dabbaghian
Affiliation:
MoCSSy Program The IRMACS Centre Simon Fraser University Burnaby, BC V5A 1S6 Canada email vdabbagh@sfu.ca
John D. Dixon
Affiliation:
School of Mathematics and Statistics Carleton University Ottawa, ON K1S 5B6 Canada email jdixon@math.carleton.ca

Abstract

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The so-called Burnside–Dixon–Schneider (BDS) method, currently used as the default method of computing character tables in GAP for groups which are not solvable, is often inefficient in dealing with groups with large centres. If $G$ is a finite group with centre $Z$ and $\lambda $ a linear character of $Z$, then we describe a method of computing the set $\mathrm{Irr} (G, \lambda )$ of irreducible characters $\chi $ of $G$ whose restriction ${\chi }_{Z} $ is a multiple of $\lambda $. This modification of the BDS method involves only $\vert \mathrm{Irr} (G, \lambda )\vert $ conjugacy classes of $G$ and so is relatively fast. A generalization of the method can be applied to computation of small sets of characters of groups with a solvable normal subgroup.

Supplementary materials are available with this article.

MSC classification

Secondary: 20C15: Ordinary representations and characters 20C40: Computational methods
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 398 - 406
Copyright
© The Author(s) 2013 

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