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The Separation Theorem for Group Actions

  • Cheryl E. Praeger
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 354)

Abstract

Let G be a group of permutations of a set Ω, and let Γ and Δ be (not necessarily distinct) subsets of Ω. Under what conditions on G, or on Γ and Δ is it possible to separate Γ from Δ by an element of G, that is to have Γ g ⋂Δ = \(\not 0\) for some gG? In 1976 Peter M. Neumann [25, Lemma 2.3] proved that every finite subset can be separated from itself in this way provided that all the G-orbits in Ω are infinite.

Keywords

Permutation Group Finite Subset Separation Theorem Transitive Group Combinatorial Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Cheryl E. Praeger
    • 1
  1. 1.University of Western AustraliaNedlandsAustralia

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