Finitary linear transformation groups and elements of finite local degree (Q1089432)

A linear transformation g of the vector space V is said to be finitary if V(g-1) is finite dimensional. The elements of GL(V) which are finitary form a normal subgroup FGL(V) (equal to GL(V) when V is finite dimensional). A representation is finitary if all elements are represented by finitary linear transformations. This paper provides a local characterization of those elements g of the group G for which there is a faithful representation of G with the image of g finitary. A consequence is that the simple group G has a faithful finitary representation if and only if each of its countable simple subgroups has a faithful finitary representation.