Normal subgroups of

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

DOI:
https://doi.org/10.1090/S0002-9939-99-05182-5

Published electronically:
October 29, 1999

MathSciNet review:
1646321

Full-text PDF

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 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:
https://doi.org/10.1090/S0002-9939-99-05182-5

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