Maximal Subgroups of Subnormal Subgroups of GL n (D) with Finite Conjugacy Classes |
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| Authors: | Dariush Kiani Mojtaba Ramezan-Nassab |
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| Institution: | 1. Department of Mathematics and Computer Science , Amirkabir University of Technology (Tehran Polytechnic) , Tehran, Iran;2. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran, Iran dkiani@aut.ac.ir;4. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran, Iran |
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| Abstract: | Let D be an infinite division ring. A famous result due to Herstein says that every noncentral element of D has infinitely many conjugates in D. So, if D* is an FC-group, then D is a field. Now let N be a subnormal subgroup of GL n (D), where n ≥ 1, and M a maximal subgroup of N. In this article, we prove that if M is an FC-group, then M is contained in the multiplicative group of some subfield of M n (D). |
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| Keywords: | Division ring FC-group Maximal subgroup Subnormal sub-group |
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