Normal subgroups of $GL_n(D)$ are not finitely generated
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- by S. Akbari and M. Mahdavi-Hezavehi
- Proc. Amer. Math. Soc. 128 (2000), 1627-1632
- DOI: https://doi.org/10.1090/S0002-9939-99-05182-5
- Published electronically: October 29, 1999
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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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Bibliographic 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
- 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
Dedicated: In memory of M. L. Mehrabadi