Some translation planes of order \(11^ 2\) which admit SL(2,9) (Q2640871)

Let G be a nonsolvable subgroup of the linear translation complement of a translation plane \(\pi\) of order \(q^ 2\) with kernel GF(q) where q is a power of a prime p, and let \(G_ 0\) be a minimal nonsolvable normal subgroup of G. There are well known results of \textit{T. G. Ostrom} [Conf. Semin. Mat. Univ. Bari 191, 29 p. (1983; Zbl 0575.51006)] and \textit{G. Mason} [Geom. Dedicata 17, 297-305 (1985; Zbl 0567.51006)] about \(G_ 0/Z(G_ 0)\). The author extends these results to the case that the kernel of \(\pi\) if GF(11). The main result is the following: Let \(\pi\) be a translation plane of dimension 2, its kernel and the linear translation complement C has a normal subgroup G such that \(G/Z(G)\cong S_ 6\). Then there are exactly three isomorphism classes of planes \(\pi\) with kernel GF(11). If D is the kernel of \(\pi\), then \(C=DG\).