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QUASIPRIMITIVE GROUPS WITH NO FIXED POINT FREE ELEMENTS OF PRIME ORDER

Published online by Cambridge University Press:  25 March 2003

MICHAEL GIUDICI
MICHAEL GIUDICI
Affiliation:
School of Mathematical Sciences, Queen Mary, London, London E1 4NS Current address: Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiagiudici@maths.uwa.edu.au
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Abstract

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 $M_{11}$ 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 ${\rm Aut}(T)$ -conjugacy class of elements of $T$ of prime order are also determined.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 73 - 84
Copyright
The London Mathematical Society, 2003

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