The structure of \(p\)-groups of finitary transformations (Q1317624)

A linear transformation of a vector space is called finitary if it acts trivially on some subspace of finite codimension. Clearly, the set of all invertible finitary transformations of a space \(V\), denoted \(\text{FGL} (V)\), is a normal subgroup of the linear group \(\text{GL}(V)\). When \(V\) has finite dimension, it is evident that \(\text{FGL} (V) = \text{GL} (V)\), but for infinite-dimensional \(V\), \(\text{FGL}(V)\) is a proper subgroup of \(\text{GL} (V)\). \(G\) is called a finitary transformation group whenever it is embeddable in \(\text{FGL} (V)\) for some vector space \(V\). In the present paper, we concentrate on the structure of \(p\)- groups of finitary transformations over a field of characteristic \(\neq p\).