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Maximal subgroups of GL n (D) with finite conjugacy classes

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Abstract

Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D * is an FC-group, then D is a field. Let M be a maximal subgroup of GL n (D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M n (D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran

    Dariush Kiani & Mojtaba Ramezan-Nassab

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Dariush Kiani

Authors
  1. Dariush Kiani
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  2. Mojtaba Ramezan-Nassab
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Correspondence to Dariush Kiani.

Additional information

This paper is dedicated to Professor M. Mahdavi-Hezavehi on the occasion of his sixtieth birthday.

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Kiani, D., Ramezan-Nassab, M. Maximal subgroups of GL n (D) with finite conjugacy classes. manuscripta math. 130, 287–293 (2009). https://doi.org/10.1007/s00229-009-0290-3

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  • DOI: https://doi.org/10.1007/s00229-009-0290-3

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