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Normal subgroups of classical groups over rings. (English) Zbl 0843.20037
The normal subgroup problem for a classical group $G$ over a ring $R$ is to study whether the “sandwich theorem” holds, i.e., for any subgroup $H$ of $G$ normalized by the elementary subgroup of $G$, there is a unique ideal $J$ of $R$, such that $H$ lies between the general and elementary congruence subgroups with respect to $J$. The authors prove that, for the pseudo-orthogonal groups over a wide class of rings, containing every ring which is finitely generated as a module over its center, the normal subgroup problem has a positive solution. It covers many previous relevant results.

20G35Linear algebraic groups over adèles and other rings and schemes
20E07Subgroup theorems; subgroup growth
20H25Other matrix groups over rings
Full Text: DOI
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