Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central
Let \(D\) be a finite-dimensional division algebra. The authors' main result is that every finitely generated subnormal subgroup of the multiplicative group of \(D\) is central. Then there are four corollaries. For example, if \(D\) is infinite, then for every positive integer \(n\), every finitely generated subnormal subgroup of \(\text{GL}(n,D)\) is central. This work extends the study of certain subgroups of \(\text{GL}(n,D)\) carried out in recent years by the first author and his collaborators in various combinations. These earlier papers are listed and, not surprisingly, used in the paper under review.
scientific article; zbMATH DE number 1429456