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The subnormal structure of general linear groups. (English) Zbl 0601.20046
{\it J. S. Wilson} [in Proc. Camb. Philos. Soc. 71, 163-177 (1972; Zbl 0237.20044)], made a fairly extensive study of normal and subnormal subgroups of a general linear group over a commutative ring. The author here takes this analysis further, firstly by tightening up certain bounds in Wilson’s work and secondly by extending the results to von Neumann regular rings and, in some cases, to rings that are Banach algebras modulo their radicals. The case of normal subgroups having been considered earlier by the author, the paper under review is primarily concerned with subnormal subgroups. The principal definitions needed to state the theorems and the theorems themselves are too lengthy and technical to quote here, and we must refer the reader to the paper itself.
Reviewer: B.A.F.Wehrfritz

MSC:
20G35Linear algebraic groups over adèles and other rings and schemes
20E15Chains and lattices of subgroups, subnormal subgroups
20E07Subgroup theorems; subgroup growth
20H25Other matrix groups over rings
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