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*.