“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 767 |
|
||||||||
| Abstract: | |||||||||
|
In this paper we study the structure of locally solvable,
solvable, locally nilpotent and nilpotent maximal subgroups of
skew linear groups. In [3] it has been conjectured that if D is
a division ring and M a nilpotent maximal subgroup of D*,
then D is commutative. In relation to this conjecture we show
that if F[M]\F contains at least an algebraic element
over F, then M is an abelian group. Also we show that
\mathbbC* ∪\mathbbC* j is a solvable maximal subgroup
of real quaternions and so give a counterexample to Conjecture 3
of [3], which states if D is a division ring and M a solvable
maximal subgroup of D*, then D is commutative. Also we
completely determine the structure of division rings with a
nonabelian algebraic locally solvable maximal subgroup, which
gives a full solution to both cases given in Theorem 8 of [3].
Ultimately, we extend our results to the general skew linear
group.
Download TeX format |
|||||||||
| back to top | |||||||||
