Regular orbits of symmetric and alternating groups

Joanna Fawcett, E.A. O'Brien, J. Saxl

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    10 Citations (Scopus)
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    © 2016 Elsevier Inc. Given a finite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs (G, V) for which G has a regular orbit on V where G is a covering group of a symmetric or alternating group and V is a faithful irreducible FG-module such that the order of F is prime and divides the order of G.
    Original languageEnglish
    Pages (from-to)21-52
    Number of pages32
    JournalJournal of Algebra
    Early online date4 Apr 2016
    Publication statusPublished - 15 Jul 2016


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