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Normal subgroups of  are not finitely generated
Author(s):
S.
Akbari;
M.
Mahdavi-Hezavehi
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1627-1632.
MSC (1991):
Primary 15A33, 16K20
Posted:
October 29, 1999
MathSciNet review:
1646321
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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  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
DOI:
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
Posted:
October 29, 1999
Dedicated:
In memory of M. L. Mehrabadi
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
2000,
American Mathematical Society
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