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Suborbits in Transitive Permutation Groups

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Combinatorics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 16))

Abstract

With any graph we can associate a group, namely its automorphism group; this acts naturally as a permutation group on the vertices of the graph. The converse idea, that of reconstructing a graph (or a family of graphs) from a transitive permutation group, has been developed by C.C. Sims, D.G. Higman, and many other people, and is the subject of the present survey. In his lecture notes [23], Higman has axiomatised the combinatorial objects that arise from permutation groups in this way, under the name coherent configurations-, but I shall discuss only the case where a group is present. My own introduction to the theory was via the unpublished paper of P.M. Neumann [30].

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Authors and Affiliations

  1. Merton College, Oxford, 0X1 4JD, England

    P. J. Cameron

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  1. P. J. Cameron
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M. Hall Jr. J. H. van Lint

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© 1975 Mathematical Centre, Amsterdam

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Cameron, P.J. (1975). Suborbits in Transitive Permutation Groups. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_20

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  • DOI: https://doi.org/10.1007/978-94-010-1826-5_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1828-9

  • Online ISBN: 978-94-010-1826-5

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