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Paper IPM / M / 163  


Abstract:  
Let D be a division ring with center F and put A=M_{n} (D)
such that either n ≥ 3 or that n=2 but D contains at least
four elements. Given a noncentral subnormal subgroup N of
A^{*}=GL_{n}(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 mth powers
of elements of A^{*} and Ω = Z(D′), where Ω is the
subgroup of the mth roots of unity in F^{*} and Z(D′) is the
center of the derived group D′ of D^{*}.
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