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A class of simple groups with no doubly transitive representations

Published online by Cambridge University Press:  09 April 2009

R. J. Clarke
R. J. Clarke
Affiliation:
Department of Pure Mathematics, University of AdelaideSouth Australia
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The first counterexample to the conjecture that all non a belian simple groups have doubly transitive permutation representations was pointed out by Parker in (1954), where he showed that the unitary groups PSU(4,4) had no doubly transitive representations. In this paper we generalize Parker's result to give an infinite class of simple groups having no doubly transitive permutation repreaentations. In this paper we generalize Parker's result to give an infinite class of simple groups having no doubly transitive permutation representations. Specifically, we prove THEOREM 1. The projective symplectic group PSp(4, q) has no doubly transitive permutation representation for q >2.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 2 , March 1975 , pp. 129 - 145
Copyright
Copyright © Australian Mathematical Society 1975

References

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