Virginia Tech
    • Log in
    View Item 
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Masters Theses
    • View Item
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Masters Theses
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Topics in Inverse Galois Theory

    Thumbnail
    View/Open
    Wills_AJ_T_2011.pdf (399.4Kb)
    Downloads: 409
    Date
    2011-04-19
    Author
    Wills, Andrew Johan
    Metadata
    Show full item record
    Abstract
    Galois theory, the study of the structure and symmetry of a polynomial or associated field extension, is a standard tool for showing the insolvability of a quintic equation by radicals. On the other hand, the Inverse Galois Problem, given a finite group G, find a finite extension of the rational field Q whose Galois group is G, is still an open problem. We give an introduction to the Inverse Galois Problem and compare some radically different approaches to finding an extension of Q that gives a desired Galois group. In particular, a proof of the Kronecker-Weber theorem, that any finite extension of Q with an abelian Galois group is contained in a cyclotomic extension, will be discussed using an approach relying on the study of ramified prime ideals. In contrast, a different method will be explored that defines rigid groups to be groups where a selection of conjugacy classes satisfies a series of specific properties. Under the right conditions, such a group is also guaranteed to be the Galois group of an extension of Q.
    URI
    http://hdl.handle.net/10919/32160
    Collections
    • Masters Theses [21565]

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us
     

     

    VTechWorks

    AboutPoliciesHelp

    Browse

    All of VTechWorksCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Log inRegister

    Statistics

    View Usage Statistics

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us