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TRANSITIVE PERMUTATION GROUPS WITHOUT SEMIREGULAR SUBGROUPS

Published online by Cambridge University Press:  24 March 2003

PETER J. CAMERON ,
MICHAEL GIUDICI ,
GARETH A. JONES ,
WILLIAM M. KANTOR ,
MIKHAIL H. KLIN ,
DRAGAN MARUšIČ  and
LEWIS A. NOWITZ
PETER J. CAMERON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS
MICHAEL GIUDICI
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS
GARETH A. JONES
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ
WILLIAM M. KANTOR
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
MIKHAIL H. KLIN
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, PO Box 653, 84105 Beer-Sheva, Israel
DRAGAN MARUšIČ
Affiliation:
IMFM, Oddelek za Matematiko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia
LEWIS A. NOWITZ
Affiliation:
2345 Broadway 526, New York, NY 10024-3213, USA
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 325 - 333
Copyright
The London Mathematical Society, 2002

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