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International Journal of Mathematics and Mathematical Sciences 
Volume 1 (1978), Issue 4, Pages 447-458
doi:10.1155/S0161171278000459

The geometry of GL(2,q) in translation planes of even order q2

N. L. Johnson

Department of Mathematics, The University of Iowa, Iowa City 52242, Iowa, USA

Received 5 August 1977; Revised 6 April 1978

Abstract

In this article we show the following: Let π be a translation plane of even order q2 that admits GL(2,q) as a collineation group. Then π is either Desarguesian, Hall or Ott-Schaeffer.