Translation Planes with an Automorphism Group Isomorphic to SL(2,5)

In this paper translation planes of odd order q, 5|q 2 -1, are constructed. Their main interest consists in the fact that their translation complement contains a group isomorphic to SL (2,5). At first these planes were obtained in other ways by O. Prohaska in the case 5|q+1 ([10], 1977) and by G. Pellegrino and G. Korchmaros in the case 5|q+1 ([9], 1982), but in both papers the Authors did not establish the previous group property. Moreover we show that Pellegrino and Korchmaros plane is not a near-field plane of order 11 2 .