Residual properties of finitary linear groups (Q1330058)

A finitary linear group is a group \(G\) of automorphisms of a vector space of infinite dimension over a field such that every element \(g \in G\) fixes elementwise a subspace of finite codimension. Let \(G\) be a finitary group. The main result of the paper under review asserts that every \(G\)-composition factor is of finite dimension provided one of the following holds: (a) \(G\) is both residually solvable and locally solvable; (b) \(G\) is residually finite, locally finite and no element of \(G\) is of order equal to the characteristic of the ground field.