Finding involutions in finite Lie type groups of odd characteristic

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    Abstract

    Let G be a finite group of Lie type in odd characteristic defined over a field with q elements. We prove that there is an absolute (and explicit) constant c such that, if G is a classical matrix group of dimension n2, then at least c/log(n) of its elements are such that some power is an involution with fixed point subspace of dimension in the interval [n/3,2n/3). If G is exceptional, or G is classical of small dimension, then, for each conjugacy class С of involutions, we find a very good lower bound for the proportion of elements of G for which some power lies in С.
    Original languageEnglish
    Pages (from-to)3397-3417
    JournalJournal of Algebra
    Volume321
    Issue number11
    DOIs
    Publication statusPublished - 2009

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