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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normal subgroups of $ GL_n(D)$
are not finitely generated


Authors: S. Akbari and M. Mahdavi-Hezavehi
Journal: Proc. Amer. Math. Soc. 128 (2000), 1627-1632
MSC (1991): Primary 15A33, 16K20
Published electronically: October 29, 1999
MathSciNet review: 1646321
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05182-5
PII: S 0002-9939(99)05182-5
Keywords: Division ring, normal subgroup, finitely generated.
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
Article copyright: © Copyright 2000 American Mathematical Society