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.
S. I. Adian (1971). On some torsion-free groups. Math. USSR. Izv.. 5, 475-484 R. Baer (1952). Endlichkeitskriterien f\"ur {K}ommutatorgruppen. Math. Ann.. 124, 161-177 R. M. Guralnick (1989). On the number of generators of a finite group. Arch. Math. (Basel). 53, 521-523 P. Hall (1956). Finite-by-nilpotent groups. Proc. Cambridge Philos. Soc.. 52, 611-616 L. A. Kurdachenko (1993). On groups with minimax conjugacy classes. Infinite groups and adjoining algebraic structures, Naukova Dumka, Kiev. , 160-177 L. A. Kurdachenko, J. Otal and I. Ya. Subbotin (2002). Groups with prescribed quotient groups
and associated module theory. World Sci. Publ., New Jersey. L. A. Kurdachenko, J. Otal and I. Ya. Subbotin (2007). Artinian modules over group
rings. Birkhauser, Basel. L. A. Kurdachenko and P. Shumyatsky The ranks of central factor and commutator groups. Math. Proc. Cambridge Phil. Soc., to appear. A. G. Kurosh (1967). The theory of groups. Nauka, Moskow. Yu. I. Merzlyakov (1964). On locally soluble groups of finite rank. Algebra i Logika. 3, 5-16 I. Schur (1904). \"Uber die Darstellungen der endlichen Gruppen durch gebrochene
lineare substitutionen. J. Reine Angew. Math.. 127, 20-50 B. A. F. Wehrfritz (1973). Infinite linear groups. Springer, Berlin.
Dixon, M. , Kurdachenko, L. and Javier, J. (2013). Linear analogues of theorems of Schur, Baer and Hall. International Journal of Group Theory, 2(1), 79-89. doi: 10.22108/ijgt.2013.2441
MLA
Dixon, M. , , Kurdachenko, L. , and Javier, J. . "Linear analogues of theorems of Schur, Baer and Hall", International Journal of Group Theory, 2, 1, 2013, 79-89. doi: 10.22108/ijgt.2013.2441
HARVARD
Dixon, M., Kurdachenko, L., Javier, J. (2013). 'Linear analogues of theorems of Schur, Baer and Hall', International Journal of Group Theory, 2(1), pp. 79-89. doi: 10.22108/ijgt.2013.2441
CHICAGO
M. Dixon , L. Kurdachenko and J. Javier, "Linear analogues of theorems of Schur, Baer and Hall," International Journal of Group Theory, 2 1 (2013): 79-89, doi: 10.22108/ijgt.2013.2441
VANCOUVER
Dixon, M., Kurdachenko, L., Javier, J. Linear analogues of theorems of Schur, Baer and Hall. International Journal of Group Theory, 2013; 2(1): 79-89. doi: 10.22108/ijgt.2013.2441
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