On quadratic GF(2)-modules for Chevalley groups over fields of odd order (Q2639957)

The purpose of this paper is to prove the following fascinating result. Let \(H=F^*(G)\) be a perfect central extension of a group of Lie type over a field of odd characteristic. Let V be an irreducible faithful GF(2)G-module and \(E\leq G\) a four-group such that \([V,E,E]=1\). Then H is isomorphic to \(L_ 2(5)\), \(L_ 2(7)\), \(L_ 2(9)\), \(3L_ 2(9)\), \(U_ 3(3)\), \({}^ 2G_ 2(3)'\), \(PSp_ 4(3)\), \(3U_ 4(3)\) or \(3^ 2U_ 4(3)\).