On the derived subgroups of certain unipotent subgroups of reductive groups over infinite fields
Let \(G\) be a connected reductive algebraic group defined over an infinite field \(F\). Let \(P\) be a minimal \(F\)-parabolic subgroup of \(G\), and \(N\) the unipotent radical of \(P\). The authors describe explicitly the derived group \(N_{\text{der}}\) of \(N\), and prove that \(N_{\text{der}}(F)=N(F)_{\text{der}}\), i.e., the group of \(F\)-rational points of \(N_{\text{der}}\) is just the derived group of the group \(N(F)\) of \(F\)-rational points of \(N\). This gives a simple description of the maximal Abelian quotient of the abstract group \(N(F)\).
scientific article; zbMATH DE number 1885649