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A note on generalised wreath product groups

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

Cheryl E. Praeger ,
C. A. Rowley  and
T. P. Speed
Cheryl E. Praeger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W.A. 6009, Australia
C. A. Rowley
Affiliation:
Mathematics Faculty, The Open University, Milton Keynes, MK7 6AA, United Kingdom
T. P. Speed
Affiliation:
CSIRO Division of Mathematics and Statistics, Box 1965 GPO, Canberra, A.C.T. 2601, Australia
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Abstract

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Generalised wreath products of permutation groups were discussed in a paper by Bailey and us. This note determines the orbits of the action of a generalised wreath product group on m–tuples (m ≥ 2) of elements of the product of the base sets on the assumption that the action on each component is m–transitive. Certain related results are also provided.

MSC classification

Secondary: 20B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 415 - 420
Copyright
Copyright © Australian Mathematical Society 1985

References

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[2]Babai, L., ‘On the abstract group of automorphisms of a graph’, pp. 1–40, Combinatorics (Temperley, , Ed.), CUP, Cambridge, 1981.Google Scholar
[3]Bailey, R. A., Praeger, Cheryl E., Rowley, C. A. and Speed, T. P., ‘Generalized wreath products of permutation groups’, Proc. London Math. Soc. (3) 47 (1983), 69–82.CrossRefGoogle Scholar
[4]Cameron, P. J., ‘Automorphism groups of graphs’, pp. 89–127, Selected topics in graph theory II (Beineke, and Wilson, , Eds.), Academic Press, London, 1983.Google Scholar
[5]Speed, T. P. and Bailey, R. A., ‘On a class of association schemes derived from lattices of equivalence relations’, pp. 55–74, Algebraic structures and applications (Schultz, , Praeger, and Sullivan, , Eds.), Marcel-Dekker, New York, 1982.Google Scholar