Cofinitary and contrafinitary linear groups (Q1915339)

Let \(V\) be a vector space over a division ring \(D\). An element \(g\neq 1\) of \(\text{GL}(V)\) is cofinitary if no infinite-dimensional subspace of \(V\) is fixed pointwise by \(g\), and is contrafinitary if no infinite-dimensional image space of \(V\) is fixed pointwise by \(g\). A subgroup of \(\text{GL}(V)\) is cofinitary (resp. contrafinitary) if each of its non-trivial elements is cofinitary (resp. contrafinitary). The author gives similarities and dissimilarities between these two types of subgroups in \(\text{GL}(V)\).