Subplanes of a translation plane

作者：Jha Vikram; Polverino Olga^*; Trombetti Rocco

来源：Finite Fields and Their Applications, 2014, 30: 121-138.

DOI：10.1016/j.ffa.2014.04.010

• Semifield
• Translation plane
• Subplane
• Derivation set

In this article we determine conditions for a finite translation plane pi in order to contain subplanes and derivation sets. We study the effects of transposition on affine subplanes of pi introducing a geometric procedure, to construct, starting from a Baer subplane pi 0 of pi, one pi(0)%26apos; lying in the transpose plane pi(t) of pi. We prove that, in general, pi(0)%26apos;; is isomorphic neither to pi 0 nor to the transpose pi(t)(0), of pi 0. Also, in the semifield case, we prove that some Knuth derivatives of the recently discovered Budaghyan-Helleseth semifield planes-are derivable and hence derive to a strict translation plane. Our analysis further shows that any plane coordinatized by a commutative Albert semifield may be embedded in a Budaghyan-Helleseth plane.

• 出版日期2014-11