Finite linear spaces admitting a two-dimensional projective linear group (Q1406735)

A linear space is called regular if every line has the same number of points. In the paper under review it is shown that if \(\text{PSL}(2,q)\), \(q > 3\), acts line transitively on a finite linear space, then there are only three possibilities for the linear space: a projective plane, a Witt-Bose-Shrikhande space or a regular linear space with parameters \((b, v, r, k) = (32760, 2080, 189, 12)\) and \(q = 2^6\). The complicated proof is divided into cases according to the parity of \(q\), the type of a point stabilizer, and the number of conjugacy classes of involutions in a line stabilizer.