Finite primitive permutation groups and regular cycles of their elements

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    Abstract

    © 2014 Elsevier Inc. We conjecture that if G is a finite primitive group and if g is an element of G, then either the element g has a cycle of length equal to its order, or for some r, m and k, the group G≤. Sym( m)wrSym( r), preserving a product structure of r direct copies of the natural action of Sym( m) or Alt( m) on k-sets. In this paper we reduce this conjecture to the case that G is an almost simple group with socle a classical group.
    Original languageEnglish
    Pages (from-to)27-55
    Number of pages29
    JournalJournal of Algebra
    Volume421
    DOIs
    Publication statusPublished - 1 Jan 2015

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