On subgroups and factor groups of GL(n, q) acting on spreads with the same characteristic

✍ Scribed by Vikram Jha

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 907 KB
• Volume: 41
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(82)90080-2

✦ Synopsis

J_et n'-. be an affine translation plane of order q' with GF(,i, in its kern. Suppose G is a subgroup of the translation complement of yr'z which leaves invariant a set A of q + 1 slopes and acts transitively on l,\A. We study the situation when G =SL(n, q) or kSL(n, q).

We show that if G 1 A = identity, then VI= is a Hall plane, a Lorimer-Rahilly plane (LR-16) or a Johnson-Walker plane (JW-16). Moreover, if n 3 3, then G fixes A elementwise and ~'5 is LR-16 or JW-16.