Division Algebras with Radicable Multiplicative Groups

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Bahari Salim, Sajad | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51314 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
Given a divisible finite field extension K/F, the structure of Br(F), the Brauer group of F, is investigated. It is shown that, if F is indivisible, then Br(F) ≃ Z_2, which generalizes the Frobenius Theorem. As a consequence, when F is indivisible, the class of all finite dimensional non-commutative F-central division algebras D having radicable multiplicative groups is determined. In fact, it is proved that the following statements are equivalent: (1) D is radicable, (2) D contains a divisible subfield K/F, and (3) D is the ordinary quaternion division algebra and F(√-1) is divisible
Keywords:
Finite Field Extension ; Division Algebra ; Division Group ; Multiplicative Group