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Pseudo-fields and doubly transitive groups

Published online by Cambridge University Press:  17 April 2009

F.W. Wilke
F.W. Wilke
Affiliation:
Department of Mathematics, University of Missouri – St Louis, St Louis, Missouri, USA.
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Abstract

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A sharply doubly transitive group which acts on a set of at least two elements is isomorphic to the group of affine transformations on a system S. This statement is true if S is replaced by either strong pseudo-field or pseudo-field. The additive system of a strong pseudo-field is a loop while the additive system of a pseudo-field need not be a loop. We show that any pseudo-field is either a strong pseudo-field or can be obtained from a strong pseudo-field in a nice way. Every near-field is a strong pseudo-field. The converse is an open question.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 2 , October 1972 , pp. 163 - 168
Copyright
Copyright © Australian Mathematical Society 1972

References

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