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

  • Part of
  • AZIZOLLAH AZAD, CHERYL E. PRAEGER
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 1 / August 2009
    Published online by Cambridge University Press:
    08 June 2009, pp. 91-104
    Print publication:
    August 2009
    • Article
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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.