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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Normal subgroups of $GL_n(D)$ are not finitely generated
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by S. Akbari and M. Mahdavi-Hezavehi PDF
Proc. Amer. Math. Soc. 128 (2000), 1627-1632 Request permission

Abstract:

As a generalization of Wedderburn’s classic theorem, it is shown that the multiplicative group of a noncommutative finite dimensional division algebra cannot be finitely generated. Also, the following conjecture is investigated: An infinite non-central normal subgroup of $GL_n(D)$ cannot be finitely generated.
References
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Additional Information
  • S. Akbari
  • Affiliation: Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran
  • Email: s_akbari@math.sharif.ac.ir
  • M. Mahdavi-Hezavehi
  • Affiliation: Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran
  • Email: mahdavi@math.sharif.ac.ir
  • Received by editor(s): January 14, 1998
  • Received by editor(s) in revised form: July 29, 1998
  • Published electronically: October 29, 1999

  • Dedicated: In memory of M. L. Mehrabadi
  • Communicated by: Ken Goodearl
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 1627-1632
  • MSC (1991): Primary 15A33, 16K20
  • DOI: https://doi.org/10.1090/S0002-9939-99-05182-5
  • MathSciNet review: 1646321