Invariant subgroups of \(^ V V\) (Q1204550)

Let \(V\) be a vector space of countably infinite dimension over the field \(F_ 2\) with two elements. The authors classify invariant subgroups which arise as kernels of certain canonical projections of the automorphism groups of totally categorical structures onto the general linear group \(GL(V)\). They first determine all invariant subgroups of \({^ V F_ 2}\) and then all closed and invariant subgroups of \({^{V\bullet}F_ 2}\). These results are used in the final section in the case of \({^ V V}\).