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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.
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