Decomposition of transvections: A theme with variations (Q1970563)

The authors describe in detail how they prove some classical results on the subgroup structure of \(\text{GL}_n(R)\) by means of a different decomposition of transvections. Next they apply their method to related situations. Amongst the topics that are being treated we find: normality of elementary subgroups, centrality of \(K_2(n,R)\) in the Steinberg group \(\text{St}(n,R)\), standard description of subgroups normalized by elementary matrices, net subgroups, subgroups of orthogonal groups, subgroups of symplectic groups, or unitary groups, or even exceptional Chevalley types.