Translation planes of even order in which the dimension has only one odd factor

Abstract

Let G be an irreducible subgroup of the linear translation complement of a finite translation plane of order qd where q is a power of 2. GF(q) is in the kernel and d=2sr where r is an odd prime. A prime factor of |G| must divide (qd+1)∏i=1d(qi−1).

Keywords

• translation planes
• collineation groups
• finite geometries.