Polynomial identities and maximal subgroups of skew linear groups |
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| Authors: | D Kiani |
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| Institution: | (1) Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran;(2) Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran |
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| Abstract: | Suppose that D is a division ring with center F and N is a non-central normal subgroup of GL
n
(D). In this paper we generalize some known results about maximal subgroups of GL
n
(D) to maximal subgroups of N. More precisely, we prove that if M is a maximal subgroup of N such that FM] satisfies a polynomial identity and  contains an algebraic element over F or  and either n ≥ 2 or n = 1 and M is not abelian, then D : F] < ∞.
This research was partially supported by a grant from IPM (No. 85160047). |
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| Keywords: | 20H25 15A33 |
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