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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 163
   School of Mathematics
  Title: Some special subgroups of GLn(D)
  Author(s):
1 . M. Mahdavi-Hezavehi
2 . S. Akbari
  Status: Published
  Journal: Algebra Colloq.
  No.: 4
  Vol.: 5
  Year: 1998
  Pages: 361-370
  Supported by: IPM
  Abstract:
Let D be a division ring with center F and put A=Mn (D) such that either n ≥ 3 or that n=2 but D contains at least four elements. Given a non-central subnormal subgroup N of A*=GLn(D), it is shown that, if N is algebraic over F, then A is algebraic over F. When D is algebraic over F, it is shown that A is algebraic over F if and only if the product of any two algebraic elements of A is algebraic over F. When D is of index m over F, it is proved that the reduced Whitehead group of A is trivial if and only if each element of reduced norm 1 can be written as a product of some m-th powers of elements of A* and Ω = Z(D′), where Ω is the subgroup of the m-th roots of unity in F* and Z(D′) is the center of the derived group D′ of D*.

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