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.

Keywords:

derived submodule of a module over a group ring , section p--rank , section ۰--rank , linear group