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dc.contributor.advisorSaltman, D. J. (David J.), 1951-en
dc.creatorHammond, John Lockwooden
dc.date.accessioned2012-10-01T20:08:42Zen
dc.date.available2012-10-01T20:08:42Zen
dc.date.issued2008-05en
dc.identifier.urihttp://hdl.handle.net/2152/18100en
dc.descriptiontexten
dc.description.abstractThis thesis is concerned with the Regular Inverse Galois Problem for p-groups over fields of characteristic unequal to p. Building upon results of Saltman, Dentzer characterized a class of finite groups that are automatically realized over every field, and proceeded to show that every group of order dividing p⁴ belongs to this class. We extend this result to include groups of order p⁵, provided that the base field k contains the p³-th roots of unity. The proof involves reducing to certain Brauer embedding problems defined over the rational function field k(x). Through explicit computation, we describe the cohomological obstructions to these embedding problems. Then by applying results about the Brauer group of a Dedekind domain, we show that they all possess solutions.en
dc.format.mediumelectronicen
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshInverse Galois theoryen
dc.subject.lcshGroup theoryen
dc.subject.lcshHomology theoryen
dc.subject.lcshBrauer groupsen
dc.subject.lcshRings (Algebra)en
dc.subject.lcshEmbeddings (Mathematics)en
dc.titleRegular realizations of p-groupsen
dc.description.departmentMathematicsen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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