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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
Mathematical Institute, University of Oxford, St Giles, Oxford, England;
R.G. Burns
Department of Mathematics, York University, Downsview, Ontario, Canada;
Sheila Oates Macdonald
Department of Mathematics, University of Queensland, St Lucia, Queensland;
Peter M. Neumann
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.

Research Article
Copyright © Australian Mathematical Society 1976


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[3]Neumann, Peter M., “The structure of finitary permutation groups”, Arch. Math. (Basel) (to appear).Google Scholar