Maximal Subgroups of, M.Sc. Thesis Sharif University of Technology ; Mahdavi Hezavehi, Mohammad (Supervisor)
Abstract
In this thesis we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [5] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of , then D is commutative. In connection with this conjecture we show that if M a nilpotent maximal subgroup of , then M is an abelian group. Also we show that is a solvable maximal subgroup of real quaternions and so give a counterexample to Conjecture 3 of [5], which states that if D is a division ring and M a solvable maximal subgroup of , then D is commutative. Also we completely determine the structure of division rings with a non-abelian...
Cataloging briefMaximal Subgroups of, M.Sc. Thesis Sharif University of Technology ; Mahdavi Hezavehi, Mohammad (Supervisor)
Abstract
In this thesis we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [5] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of , then D is commutative. In connection with this conjecture we show that if M a nilpotent maximal subgroup of , then M is an abelian group. Also we show that is a solvable maximal subgroup of real quaternions and so give a counterexample to Conjecture 3 of [5], which states that if D is a division ring and M a solvable maximal subgroup of , then D is commutative. Also we completely determine the structure of division rings with a non-abelian...
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