Linear groups containing a root subgroup
Let \(k\) be a field of characteristic not 2, \(k\neq\text{GF}(3)\), \(\text{GF}(9)\), and \(K\) an algebraic extension of \(k\). Let \(G\) be an irreducible subgroup of \(\text{GL}_n(K)\) (\(n\geq 2\)). The author proves that if \(G\) contains a root \(k\)-subgroup then, for some integers \(m\) and \(r\) with \(mr=n\), \(G\) contains a normal subgroup which is conjugate to the \(r\)th Cartesian product of a classical (special linear, special unitary, or symplectic) group of dimension \(m\) over a field between \(k\) and \(K\).
scientific article; zbMATH DE number 1023882