Irreducible representations of periodic finitary linear groups (Q1911625)

Let \(K\) be a field and \(V\) a vector space of infinite dimension over \(K\). The elements \(g\in\text{Aut}_K(V)\) such that \(\dim(g-\text{Id})V<\infty\) form a group \(\text{FGL}(V)\) called finitary linear. Let \(K_0\) denote the algebraic closure of the prime subfield of \(K\) in \(K\). Let \(G\subset\text{FGL}(V)\) be a periodic subgroup. The main theorem says that there is a basis \(B\) of \(V\) such that the matrices of \(G\) with respect to \(B\) have their entries in \(K_0\).