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A note on doubly transitive groups

Published online by Cambridge University Press:  09 April 2009

Peter Lorimer
Peter Lorimer
Affiliation:
University of AucklandAuckland, New Zealand
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W. Feit [1], N. Itô [2] and M. Suzuki [3] have determined all doubly transitive groups with the property that only the identity fixes three symbols. It is of interest to the theory of projective planes to determine whether any of these groups contain a sharply doubly transitive subset (see Definition 1). It is found that if such a group G contains such a subset R then R is a normal subgroup of G, i.e. R is a doubly transitive normal subgroup of G in which only the identity fixes two symbols.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 4 , November 1966 , pp. 449 - 451
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Feit, W., ‘On a class of doubly transitive permutation groups’, Illinois J. Math. 4 (1960), 170–186.CrossRefGoogle Scholar
[2]Itô, N., ‘On a class of doubly transitive permutation groups’, Illinois J. Math. 6 (1962), 341–352.CrossRefGoogle Scholar
[3]Suzuki, M., ‘On a class of doubly transitive groups’, Ann. of Math. 75 (1962), 105–145.Google Scholar