Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 25
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Burness, Timothy C. and Tong-Viet, Hung P. 2016. Primitive permutation groups and derangements of prime power order. Manuscripta Mathematica, Vol. 150, Issue. 1-2, p. 255.

    Giudici, Michael Morgan, Luke Potočnik, Primož and Verret, Gabriel 2015. Elusive groups of automorphisms of digraphs of small valency. European Journal of Combinatorics, Vol. 46, p. 1.

    Hujdurović, Ademir Kutnar, Klavdija and Marušič, Dragan 2015. Vertex-transitive generalized Cayley graphs which are not Cayley graphs. European Journal of Combinatorics, Vol. 46, p. 45.

    Kovács, István Malnič, Aleksander Marušič, Dragan and Miklavič, Štefko 2015. Transitive group actions: (im)primitivity and semiregular subgroups. Journal of Algebraic Combinatorics, Vol. 41, Issue. 3, p. 867.

    Jones, John and Roberts, David 2014. The tame-wild principle for discriminant relations for number fields. Algebra & Number Theory, Vol. 8, Issue. 3, p. 609.

    SPIGA, PABLO 2014. Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 157, Issue. 01, p. 45.

    Burness, Timothy C. Giudici, Michael and Wilson, Robert A. 2011. Prime order derangements in primitive permutation groups. Journal of Algebra, Vol. 341, Issue. 1, p. 158.

    Dobson, Edward and Marušič, Dragan 2011. On Semiregular Elements of Solvable Groups. Communications in Algebra, Vol. 39, Issue. 4, p. 1413.

    Giulietti, Massimo and Korchmáros, Gábor 2010. On cyclic semi-regular subgroups of certain 2-transitive permutation groups. Discrete Mathematics, Vol. 310, Issue. 22, p. 3058.

    Kutnar, Klavdija and Šparl, Primož 2010. Distance-transitive graphs admit semiregular automorphisms. European Journal of Combinatorics, Vol. 31, Issue. 1, p. 25.

    Saražin, Marko Lovrečič and Marušič, Dragan 2010. Vertex-transitive expansions of (1, 3)-trees. Discrete Mathematics, Vol. 310, Issue. 12, p. 1772.

    Xu, Jing 2010. Vertex-transitive tournaments of order a product of two distinct primes. Journal of Group Theory, Vol. 13, Issue. 4,

    Zhou, Jin-Xin and Feng, Yan-Quan 2010. On symmetric graphs of valency five. Discrete Mathematics, Vol. 310, Issue. 12, p. 1725.

    Giudici, Michael and Kelly, Shane 2009. Characterizing a family of elusive permutation groups. Journal of Group Theory, Vol. 12, Issue. 1,

    Kutnar, Klavdija and Marušič, Dragan 2009. Hamilton cycles and paths in vertex-transitive graphs—Current directions. Discrete Mathematics, Vol. 309, Issue. 17, p. 5491.

    Xu, Jing 2009. On Elusive Permutation Groups of Square-Free Degree. Communications in Algebra, Vol. 37, Issue. 9, p. 3200.

    Xu, Jing 2008. Semiregular automorphisms of arc-transitive graphs with valency <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:mi>p</mml:mi><mml:mi>q</mml:mi></mml:math>. European Journal of Combinatorics, Vol. 29, Issue. 3, p. 622.

    Dobson, Edward Malnič, Aleksander Marušič, Dragan and Nowitz, Lewis A. 2007. Minimal normal subgroups of transitive permutation groups of square-free degree. Discrete Mathematics, Vol. 307, Issue. 3-5, p. 373.

    Dobson, Edward Malnič, Aleksander Marušič, Dragan and Nowitz, Lewis A. 2007. Semiregular automorphisms of vertex-transitive graphs of certain valencies. Journal of Combinatorial Theory, Series B, Vol. 97, Issue. 3, p. 371.

    Giudici, Michael 2007. New Constructions of Groups Without Semiregular Subgroups. Communications in Algebra, Vol. 35, Issue. 9, p. 2719.

  • Journal of the London Mathematical Society, Volume 66, Issue 2
  • October 2002, pp. 325-333


  • DOI:
  • Published online: 01 March 2003

A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups are also included. In a sequel, Giudici has determined all the quasiprimitive elusive groups.

Part of the motivation for studying this class of groups was a conjecture due to Marušič, Jordan and Klin asserting that there is no elusive 2-closed permutation group. It is shown that the constructions given will not build counterexamples to this conjecture.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *