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

1976/02/01 by B.J. Birch, B. J. Birch, R.G. Burns +4 · 6 citations
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Finite Group Theory Research #Coding theory and cryptography

paper · pdf · doi:10.1017/s0004972700024813

Abstract

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 .

Citations

• The structure of finitary permutation groups

Cited by

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• Separating subsets from their images
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• Multicoloured Random Graphs: Constructions and Symmetry
• Free actions of free groups on countable structures and property (T)

Related

• Permutation Groups and Orbits on Power Sets
• Finite Permutation Groups with Few Orbits Under the Action on the Power Set
• On some combinatorial properties of the orbits on subsets
• Finite transitive permutation groups with only small normaliser orbits
• Orbit-equivalent infinite permutation groups