Linear analogues of theorems of Schur, Baer and Hall

Document Type: Ischia Group Theory 2012

Authors

1 University of Alabama

2 National University of Dnepropetrovsk

3 University of Zaragoza

Abstract

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.

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