Show simple item record

dc.contributor.authorWills, Andrew Johanen
dc.date.accessioned2014-03-14T20:34:56Zen
dc.date.available2014-03-14T20:34:56Zen
dc.date.issued2011-04-19en
dc.identifier.otheretd-05032011-124510en
dc.identifier.urihttp://hdl.handle.net/10919/32160en
dc.description.abstractGalois 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.en
dc.publisherVirginia Techen
dc.relation.haspartWills_AJ_T_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectKronecker-Weber Theoremen
dc.subjectRigid Groupsen
dc.subjectInverse Galois Theoryen
dc.titleTopics in Inverse Galois Theoryen
dc.typeThesisen
dc.contributor.departmentMathematicsen
dc.description.degreeMaster of Scienceen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelmastersen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairBrown, Ezra A.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberLoehr, Nicholas A.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05032011-124510/en
dc.date.sdate2011-05-03en
dc.date.rdate2011-05-19en
dc.date.adate2011-05-19en


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record