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Pseudo-fields and doubly transitive groups
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1972
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