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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A property of the groups $ P\Gamma L(m,\,q)$, $ q\geq 5$


Author: Peter Lorimer
Journal: Proc. Amer. Math. Soc. 37 (1973), 393-396
MSC: Primary 20H15; Secondary 20B20, 50A15
MathSciNet review: 0313415
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Abstract: It is well known that the existence of a sharply doubly transitive set of permutations is equivalent to the existence of a projective plane. The natural representation of the group $ P\Gamma L(m,q),m \geqq 2$, is doubly transitive and it is proved here that this permutation group does not contain a sharply doubly transitive subset when $ q \geqq 5$.


References [Enhancements On Off] (What's this?)

  • [1] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703 (37 #302)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313415-0
PII: S 0002-9939(1973)0313415-0
Article copyright: © Copyright 1973 American Mathematical Society