Changing the field characteristic on finitary linear groups (Q1383571)

Let \(V\) be a vector space over the (commutative) field \(F\). The finitary general linear group on \(V\) is \(\text{FGL}(V)=\{g\in\Aut_FV:\dim_FV(g-1)<\infty\}\). Suppose \(\text{char }F=p>0\) and let \(G\) be a periodic \(p'\)-subgroup of \(\text{FGL}(V)\). The author proves that \(G\) is isomorphic to a finitary linear group \(G_0\) over some field of characteristic zero. Moreover, if \(G\) is irreducible as a subgroup of \(\text{FGL}(V)\), then \(G_0\) can also be chosen to be irreducible. This extends well-known results about finite linear groups, for example. The author's proof makes critical use of ultraproducts.