Subgrupos congruentes de grupos clássicos
DOI:
https://doi.org/10.5433/1679-0375.1989v10n4p249Keywords:
Groups and rings, Glogal field, Theory of congruence of matrices, Linear álgebra in integral domain.Abstract
We calculate the Índices of congruence subgroups, SIn(D,I), GIn(D,I), Spn(D,I) e Spn(D,I) of special linear group SIn(D), general linear group GIn{D), simpletic group Spn(D) and orthogonal group Son(D), respectively. Here I is an ideal of D, the ring of integer of a global field K. The Othogonal group Son(D) is taken over quadratic form. For technical reasons, in the Induction process, all ideais of D are assumed to be principal for n = 2, in the ortogonal case. We also study the profectiom maps from SIn(D), GIn(D), Spn(D) and Son(D) to corresponding groups , SIn(D/l), Gln(D/l), Spn(D/I) and Son(D/I). defined over quocient ring D/I. A generating set for each of these groups is also determined.
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