On nonmodular periodic finitary linear groups (Q1969128)

Let \(V\) be a vector space over a field \(F\) of prime characteristic \(p\) and \(G\) a periodic \(p'\)-subgroup of the finitary general linear group \(\text{FGL}(V)\). \textit{M. S. Lucido} [Arch. Math. 70, No. 2, 97-103 (1998; Zbl 0897.20035)] proved that there is a finitary linear group \(G_0\) over a field of characteristic 0 that is isomorphic to \(G\). Moreover, if \(G\) is irreducible, then \(G_0\) can be chosen to be irreducible. The author provides an alternative proof of Lucido's result, which is somewhat shorter, more explicit and more elementary. Further, the author generalizes this result to periodic finitary skew linear \(p'\)-groups of characteristic \(p\), i.e., replaces fields by division rings in the hypotheses.