Isomorphisms of groups full of projective transvections (Q1078673)

\textit{O. T. O'Meara} [J. Algebra 44, 93-142 (1977; Zbl 0356.15002)] gave a description of isomorphisms between full subgroups of the groups \(P\Gamma L(V_ 1)\), \(P\Gamma L(V_ 2)\), i.e. subgroups full of projective transvections, where \(V_ i\) is a vector space over a skew field of dimension \(\geq 5\), \(i=1,2\), and \textit{Yu. V. Sosnovskij} [in the book: Isomorphisms of classical groups over integral domains, Moscow, Mir, 259- 268 (1980; Zbl 0447.20037)] has extended this description to dimensions dim \(V_ i\geq 3:\) all automorphisms under consideration turned out to be standard. A new and shorter proof of the O'Meara-Sosnovskij theorem is given in this article.