
doi: 10.1007/bf01193629
Let \(\pi\) be a translation plane of order \(q^ d\), with kernel GF(q). The paper being corrected [Arch. Math. 47, 568-572 (1986; Zbl 0588.51003)] was an attempt to improve on earlier results to the effect that if the translation complement contains an elementary Abelian group of order \(2^ c\), then \(2^{c-2}\) divides d. Our proof was based on some tacit unjustified assumptions and hence is incorrect. The following now appears to be a fundamental question for the theory of finite translation planes: ``Is there a translation plane of order \(q^ 4\), where q is prime to two and three such that the translation complement contains a quaternion group of order q whose fixed point subspace is a subplane of order q?''
Translation planes and spreads in linear incidence geometry, Finite automorphism groups of algebraic, geometric, or combinatorial structures, translation plane, Finite affine and projective planes (geometric aspects), translation complement, 2-group
Translation planes and spreads in linear incidence geometry, Finite automorphism groups of algebraic, geometric, or combinatorial structures, translation plane, Finite affine and projective planes (geometric aspects), translation complement, 2-group
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