“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 163 |
|
||||
| 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*.
Download TeX format |
|||||
| back to top | |||||
