A structure theory for two-dimensional translation planes of order q2 that admit collineation groups of order q2

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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