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

Autor:	Azizollah Azad, Cheryl E. Praeger
Rok vydání:	2009
Předmět:	Set (abstract data type) Combinatorics Discrete mathematics Cardinality Group (mathematics) General Mathematics Maximal torus Pairwise comparison General linear group Unipotent Element (category theory) Mathematics
Zdroj:	Bulletin of the Australian Mathematical Society. 80:91-104
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972709000057
Popis:	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.
Databáze:	OpenAIRE
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