Identify Cross Product Division Algebra

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Daryaei, Ali | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48624 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
In the present thesis, we study on the structure of the solvable, supersoluble, nilpotent, and irreducible structures of the subgroups. The main purpose of the present thesis is to represent a criterion given for D to be a supersoluble (nilpotent) crossed product division algebra in terms of subgroup of the multiplicative group D* of D. It is shown that the D is supersoluble (nilpotent) crossed product, if and only if D* contains an irreducible abelian-by-supersoluble (nilpotent) subgroup. Furtetmore, we review and discuss the structure of the crossed product division algebra, D, with the solvable irreducible subgroup, D*, and finally we extend our results for the semi-cross product of the division algebra
Keywords:
Division Algebra ; Crossed Product ; Soluble Subgroups ; Nilpotent Supgroup ; Irreducible Left Subalgebras ; Abelian-by-Super Soluble Subgroup

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