A family of translation planes of orderq2m+1with two orbits of length 2 andq2m+1−1 onl∞

✍ Scribed by Chihiro Suetake

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 822 KB
• Volume: 42
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147547

✦ Synopsis

A class of translation planes of order q2rn+l, where q is an odd prime power and m/> 1, is constructed. If m= 1, then this class is contained in the class of order q3 constructed by Hiramine I-5]. These planes of order q2m+~ are of dimension 2m+l over their kernels. If q2m+~ ~ 33, then the linear translation complements of these planes have two orbits of length 2 and q2m+ ~ _ 1 on l® and this class contains many planes which are not generalized Andr6 planes. If q2m + t= 33, then each plane of this class is isomorphic to the Hering plane of order 27.