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Sharply two-transitive families of permutations on an immune set

Published online by Cambridge University Press:  09 April 2009

J. C. E. Dekker
J. C. E. Dekker
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey 08903, U.S.A.
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Abstract

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It is known that there is a finite affine (or projective) plane of order n if and only if there is a sharply two-transitive set of permutations of degree n. This paper deals with a generalization of this theorem, in which finite sets are replaced by isolated sets, cardinalities by isols and certain effectiveness conditions are imposed on the two systems involved which are trivially satisfied in the finite case.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 02F40, secondary 05B25.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 362 - 374
Copyright
Copyright © Australian Mathematical Society 1978

References

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