Linear analogues of theorems of Schur, Baer and Hall

A celebrated result of I. Schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the Theory of Groups. In this paper we exhibit a similar result to Schur's Theorem for vector spaces, acted upon by certain groups. The proof of this analogous result depends on the characteristic of the underlying field. We also give linear versions of corresponding theorems of R. Baer and P. Hall.