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Solvability of a Class of Rank 3 Permutation Groups1)

Published online by Cambridge University Press:  22 January 2016

D.G. Higman
D.G. Higman*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan
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1. Introduction. Let G be a rank 3 permutation group of even order on a finite set X, |X| = n, and let Δ and Γ be the two nontrivial orbits of G in X×X under componentwise action. As pointed out by Sims [6], results in [2] can be interpreted as implying that the graph = (X, Δ) is a strongly regular graph, the graph theoretical interpretation of the parameters k, l, λ and μ of [2] being as follows: k is the degree of , λ is the number of triangles containing a given edge, and μ is the number of paths of length 2 joining a given vertex P to each of the l vertices ≠ P which are not adjacent to P. The group G acts as an automorphism group on and on its complement = (X,Γ).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971 , pp. 89 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

Footnotes

1)

Research supported in part by the National Science Foundation.

References

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[3] Higman, D.G.: Primitive rank 3 groups with a prime subdegree. Math. Z. 91 (1966), 70–86.Google Scholar
[4] Higman, D.G.: Intersection matrices for finite permutation groups. J. Alg. 6 (1967), 22–42.Google Scholar
[5] C.C. Sims Graphs and finite permutation groups. Math. Z. 95 (1967), 76–86.CrossRefGoogle Scholar
[6] C.C. Sims Graphs with rank 3 automorphism groups. J. Comb. Theory (to appear).Google Scholar
[7] Wielandt, H.: Finite permutation groups. New York: Academic Press 1964.Google Scholar