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Dixon, Martyn, Kurdachenko, Leonid, Javier, Javier. (1391). Linear analogues of theorems of Schur, Baer and Hall. , 2(1), 79-89. doi: 10.22108/ijgt.2013.2441
Martyn Dixon; Leonid Kurdachenko; Javier Javier. "Linear analogues of theorems of Schur, Baer and Hall". , 2, 1, 1391, 79-89. doi: 10.22108/ijgt.2013.2441
Dixon, Martyn, Kurdachenko, Leonid, Javier, Javier. (1391). 'Linear analogues of theorems of Schur, Baer and Hall', , 2(1), pp. 79-89. doi: 10.22108/ijgt.2013.2441
Dixon, Martyn, Kurdachenko, Leonid, Javier, Javier. Linear analogues of theorems of Schur, Baer and Hall. , 1391; 2(1): 79-89. doi: 10.22108/ijgt.2013.2441

Linear analogues of theorems of Schur, Baer and Hall

International Journal of Group Theory
مقاله 7، دوره 2، شماره 1، خرداد 2013، صفحه 79-89    اصل مقاله (433.09 K)
نوع مقاله: Ischia Group Theory 2012
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2441
نویسندگان
Martyn Dixon* 1؛ Leonid Kurdachenko2؛ Javier Javier3
1University of Alabama
2National University of Dnepropetrovsk
3University of Zaragoza
چکیده
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.
کلیدواژه‌ها
derived submodule of a module over a group ring؛ section $p$--rank؛ section $0$--rank؛ linear group
مراجع
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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
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