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On Rank 3 Groups Having λ = 0

Published online by Cambridge University Press:  20 November 2018

M. D. Atkinson
M. D. Atkinson*
Affiliation:
University College, Cardiff, U.K.
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In this paper we shall consider certain rank 3 permutation groups G which act on a set Ω of size n. Thus a point stabiliser Gα will have 3 orbits { α }, △ (α), Γ (α) of sizes 1, k, I respectively. It is well known that, if |G| is even, then the orbital △ defines a strongly regular graph on Ω. In this graph, every point has valency k, every pair of adjacent points are adjacent to a constant number λ of common points, and every pair of non-adjacent points are adjacent to a constant number μ of common points. This notation is reasonably standard (see [4], where much background theory is given).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 845 - 847
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Atkinson, M. D., Rank 3 permutation groups with X = 0, Unpublished manuscript, Cardiff 1975.Google Scholar
2. Cameron, P. J. and J. H. van Lint, Graph theory, coding theory and block designs, London Math. Soc. Lecture Note Series 19 (Cambridge University Press 1975).Google Scholar
3. Cameron, P. J., Permutation groups with multiply transitive suborbits, Proc. London Math. Soc. (3) 25 (1972), 427–440.Google Scholar
4. Hestenes, M. D. and D. G. Higman. Rank 8 groups and strongly regular graphs, SIAM-AMS Proc. IV, Computers in Algebra and Number Theory (1971), 141–159.Google Scholar
5. Sims, C. C., Primitive groups, graphs and block designs, Annals of New York Academy of Sciences 175, Article 1 (1970), 351–353.Google Scholar