On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices

✍ Scribed by Bui Xuan Hai

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 866 KB
• Volume: 121
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00051-5

✦ Synopsis

For an arbitrary division algebra T we study the arrangement of subgroups of the special linear group r = SL.(T)(n 2 3) that contain the subgroup A = SD,(T) of diagonal matrices with Dieudonne's determinant (see [l]) equal to 1. We show that the description of these subgroups is standard in the following sense: For any subgroup H, A < H 5 r there exists a unique D-net D such that T(o) 5 H 2 Nr(o), where T(u) is the D-net subgroup corresponding to the net cr and Nr(o) is the normalizer of r(o) in r. @