On collineation groups of translation planes of order q4

Abstract

Let P be an affine translation plane of order q4 admitting a nonsolvable group G in its translation complement. If G fixes more than q+1 slopes, the structure of G is determined. In particular, if G is simple then q is even and G=L2(2s) for some integer s at least 2.

Keywords

• translation planes
• nonsolvable groups.