Generic 2-coverings of finite Groups of Lie type

A causa di problemi di formattazione, che impediscono l'inserimento di simboli matematici, quello che segue e' solo una sintesi del vero abstract, per il quale si rimanda al pdf del paper. It was shown by R.H.Dye that in a symplectic group G, defined over a finite field of characteristic 2, every element in G stabilizes a quadratic form of maximal or non-maximal Witt index inducing the corresponding bilinear form. Thus G is the union of the two G-conjugacy classes of orthogonal subgroups (+ and -) embedded naturally. In this paper we classify all finite groups of Lie type with this generic 2-covering property (Thm.A). In particular, we show that there exists also an interesting example in characteristic 3.