Maximal Subgroups of

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Ghasemi, Mohammad | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42174 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
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 algebraic locally solvable maximal subgroup. Ultimately, we extend our results to the general skew linear groups.
Keywords:
Soluble Subgroups ; Maximal Subgroup ; Division Rings ; Skew Linear Group ; Nilpotent Supgroup