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Journal of the London Mathematical Society 2003 67(1):73-84; doi:10.1112/S0024610702003812
© 2003 by London Mathematical Society
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© The London Mathematical Society

Quasiprimitive Groups with No Fixed Point Free Elements of Prime Order

Michael Giudici

School of Mathematical Sciences, Queen Mary, London London E1 4NS

Received 24 April 2001. Revision received 17 January 2002.

The paper determines all permutation groups with a transitive minimal normal subgroup that have no fixed point free elements of prime order. All such groups are primitive and are wreath products in a product action involving M11 in its action on 12 points. These groups are not 2-closed and so substantial progress is made towards asserting the truth of the polycirculant conjecture that every 2-closed transitive permutation group has a fixed point free element of prime order. All finite simple groups T with a proper subgroup meeting every Aut(T)-conjugacy class of elements of T of prime order are also determined.

Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia, giudici{at}maths.uwa.edu.au


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