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The Quarterly Journal of Mathematics Advance Access published online on June 27, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap021
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

SEMIFIELDS AS FREE MODULES1

Mashhour I. Al-Ali 2{dagger}

Department of Mathematics, Zarqa Private University, Zarqa, Jordan

{dagger} E-mail: mashhour_ibrahim{at}yahoo.com

Received 16 November 2007; Accepted for publication 2 May 2009.


  Abstract

The aim of this paper is to prove that, if S is a finite semifield over a finite field, and E is an elementary abelian 2-group of automorphisms, then E acts freely on S. Moreover, if E acts freely of rank 1 and if S has even order, then |E| ≤ 4.

1 This work has been done during the sabbatical leave at Zarqa Private University.

2 Permanent address: Department of Mathematics, Mu'tah University, P.O. Box 7, Al-Karak, Jordan.


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