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A structure theory for two-dimensional translation planes of order q 2 that admit collineation groups of order q 2 |
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| Authors: | Mauro Biliotti Vikram Jha Norman L. Johnson Giampaolo Menichetti |
| Affiliation: | (1) Dipartimento di Matematica, Università di Lecce, Via Arnesano, 73100 Lecce, Italia;(2) Department of Mathematics, Glasgow College of Technology, Cowcaddens Road, G4 0BA Glasgow, U.K.;(3) Department of Mathematics, The University of Iowa, 52242 Iowa City, Iowa, U.S.A.;(4) Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italia |
| Abstract: | This paper is devoted to the study of translation planes of order q2 and kernel GF(q) that admit a collineation group of order q2 in the linear translation complement. We give a representation of this group by a suitable set of matrices depending on some functions over GF(q). Using this representation we obtain several results concerning the existence and the collineation group of the plane. |
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