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Transitive permutation groups without semiregular subgroups

Transitive permutation groups without semiregular subgroups
Transitive permutation groups without semiregular subgroups
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 Marušic, 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.
0024-6107
325-333
Cameron, P.J.
4a77d54f-5e2e-4fea-a7e0-5401cd9131df
Guidici, M.
4acf6f9a-4207-4c1b-ac38-de724d0eca21
Jones, G.A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Kantor, W.M.
40ce4091-5d7b-4188-8f80-81734c071a25
Klin, M.H.
183a4e44-e9a2-431d-8608-1302711db8cb
Marusic, D.
488312fe-caff-41cf-a1e3-ef5d3a7a5889
Nowitz, L. A.
c3604867-44a7-4298-9625-27dbdb6529b3
Cameron, P.J.
4a77d54f-5e2e-4fea-a7e0-5401cd9131df
Guidici, M.
4acf6f9a-4207-4c1b-ac38-de724d0eca21
Jones, G.A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Kantor, W.M.
40ce4091-5d7b-4188-8f80-81734c071a25
Klin, M.H.
183a4e44-e9a2-431d-8608-1302711db8cb
Marusic, D.
488312fe-caff-41cf-a1e3-ef5d3a7a5889
Nowitz, L. A.
c3604867-44a7-4298-9625-27dbdb6529b3

Cameron, P.J., Guidici, M., Jones, G.A., Kantor, W.M., Klin, M.H., Marusic, D. and Nowitz, L. A. (2002) Transitive permutation groups without semiregular subgroups Journal of the London Mathematical Society, 66, (2), pp. 325-333. (doi:10.1112/S0024610702003484).

Record type: Article

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 Marušic, 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.

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Published date: 2002

Identifiers

Local EPrints ID: 41172
URI: http://eprints.soton.ac.uk/id/eprint/41172
ISSN: 0024-6107
PURE UUID: 09833247-5e1d-44d3-a94b-19bd1bbe4872

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Date deposited: 25 Jul 2006
Last modified: 17 Jul 2017 15:32

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Contributors

Author: P.J. Cameron
Author: M. Guidici
Author: G.A. Jones
Author: W.M. Kantor
Author: M.H. Klin
Author: D. Marusic
Author: L. A. Nowitz

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