Linear groups generated by two-dimensional elements of order r\(\geq 5\) (Q1079666)

An element \(x\in SL(n,P)\) is called a two-dimensional element if it has Jordan form \(diag(\epsilon,\epsilon^{-1},1,...,1)\), \(\epsilon\) \(\neq 1\); P is an algebraically closed field. The following theorem is proved: Assume that \(G<SL(n,P)\) is a finite irreducible group generated by two- dimensional elements of order \(r\geq 5\), char P\(=p>7\). If G does not contain p-elements, and under the condition that rank(u-1)\(\leq 2\), then \(n\leq 4\) and G lifts to characteristic 0.