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On the orbit-sizes of permutation groups containing elements separating finite subsets

Published online by Cambridge University Press:  17 April 2009

B.J. Birch ,
R.G. Burns ,
Sheila Oates Macdonald  and
Peter M. Neumann
B.J. Birch
Affiliation:
Mathematical Institute, University of Oxford, St Giles, Oxford, England;
R.G. Burns
Affiliation:
Department of Mathematics, York University, Downsview, Ontario, Canada;
Sheila Oates Macdonald
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland;
Peter M. Neumann
Affiliation:
Queen's College, Oxford, England.
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It is proved that if G is a permutation group on a set Ω every orbit of which contains more than mn elements, then any pair of subsets of Ω containing m and n elements respectively can be separated by an element of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 1 , February 1976 , pp. 7 - 10
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Neumann, B.H., “Groups covered by permutable subsets”, J. London Math. Soc. 29 (1954), 236–248.CrossRefGoogle Scholar
[2]Neumann, B.H., “Groups covered by finitely many cosets”, Publ. Math. Debrecen 3 (1953–54), 227–242 (1955).CrossRefGoogle Scholar
[3]Neumann, Peter M., “The structure of finitary permutation groups”, Arch. Math. (Basel) (to appear).Google Scholar