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MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF THREE-DIMENSIONAL GENERAL LINEAR GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 June 2009

AZIZOLLAH AZAD  and
CHERYL E. PRAEGER
AZIZOLLAH AZAD*
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran (email: a-azad@sci.ui.ac.ir, a-azad@araku.ac.ir)
CHERYL E. PRAEGER
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia (email: praeger@maths.uwa.edu.au)
*
✉For correspondence; e-mail: a-azad@sci.ui.ac.ir,a-azad@araku.ac.ir
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Abstract

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Let G be a group. A subset N of G is a set of pairwise noncommuting elements if xy⁄=yx for any two distinct elements x and y in N. If ∣N∣≥∣M∣ for any other set of pairwise noncommuting elements M in G, then N is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements in a three-dimensional general linear group. Moreover, we show how to modify a given maximal subset of pairwise noncommuting elements into another maximal subset of pairwise noncommuting elements that contains a given ‘generating element’ from each maximal torus.

Keywords

singer cycle subgroupunipotent elementgeneral linear group

MSC classification

Secondary: 20D60: Arithmetic and combinatorial problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 91 - 104
Copyright
Copyright © Australian Mathematical Society 2009

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