In [10] it was shown by R.H. Dye that in a symplectic group G :=Sp_{2l}(2^f) = Iso (V ; (.,.)) 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 bilinear form (.,.). Thus G is the union of the two G-conjugacy classes of subgroups isomorphic to O_{2l}^+(2^f ) and O_{2l}^-(2^f ) embedded naturally. In this paper we classify all finite groups of Lie type (G;F) with this generic 2- covering property (Thm. A). In particular, we will show that there exists also an interesting example in characteristic 3, i.e., in the finite group of Lie type G := F_4(3^f ) every element in G is conjuagte to an element of the subgroup B_4(3^f ) < F_4(3^f ) or of the subgroup 3:^3D_4(3^f ) < F_4(3^f).

Bubboloni, D., Lucido, M., Weigel, T. (2006). Generic 2-coverings of finite groups of lie type. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 115, 209-252.

Generic 2-coverings of finite groups of lie type

WEIGEL, THOMAS STEFAN
2006

Abstract

In [10] it was shown by R.H. Dye that in a symplectic group G :=Sp_{2l}(2^f) = Iso (V ; (.,.)) 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 bilinear form (.,.). Thus G is the union of the two G-conjugacy classes of subgroups isomorphic to O_{2l}^+(2^f ) and O_{2l}^-(2^f ) embedded naturally. In this paper we classify all finite groups of Lie type (G;F) with this generic 2- covering property (Thm. A). In particular, we will show that there exists also an interesting example in characteristic 3, i.e., in the finite group of Lie type G := F_4(3^f ) every element in G is conjuagte to an element of the subgroup B_4(3^f ) < F_4(3^f ) or of the subgroup 3:^3D_4(3^f ) < F_4(3^f).
Articolo in rivista - Articolo scientifico
finite groups, maximal subgroups
English
2006
115
209
252
none
Bubboloni, D., Lucido, M., Weigel, T. (2006). Generic 2-coverings of finite groups of lie type. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 115, 209-252.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/2397
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