Normalizers and self-normalizing subgroups II

作者：Sirola Boris^*

来源：Central European Journal of Mathematics, 2011, 9(6): 1317-1332.

DOI：10.2478/s11533-011-0091-2

• Normalizer
• Self-normalizing subgroup
• Centralizer
• Symplectic group
• Even orthogonal group
• Odd orthogonal group

Let K be a field, G a reductive algebraic K-group, and G(1) <= G a reductive subgroup. For G(1) <= G, the corresponding groups of K-points, we study the normalizer N = N-G(G(1)). In particular, for a standard embedding of the odd orthogonal group G(1) = SO(m, K) in C = SL(m, K) we have N congruent to G(1) x mu(m)(K), the semidirect product of G(1) by the group of m-th roots of unity in K. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, K) were computed in [Sirola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = CL(m K) and G(1) = O(m, K) we have N congruent to G(1) x K-x. In both of these cases, N is a self-normalizing subgroup of G.

• 出版日期2011-12