Transitive permutation groups without semiregular subgroups

Peter J. Cameron, Michael Giudici, Gareth A. Jones, William M. Kantor, Mikhail H. Klin, Dragan Marušič, Lewis A. Nowitz

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

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 Marus�ic�, 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.

Original languageEnglish
Pages (from-to)325-333
Number of pages9
JournalJournal of the London Mathematical Society
Volume66
Issue number2
DOIs
StatePublished - 1 Jan 2002

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