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dc.contributor.advisorWu, Qingquan
dc.contributor.committeeChairWu, Qingquan
dc.contributor.committeeMemberKhasawneh, Mahmoud
dc.contributor.committeeMemberLin, Runchang
dc.contributor.committeeMemberMilovich, David
dc.creatorCastaneda, Jeffrey Anthony 2014
dc.description.abstractWe investigate the ramification group filtration of a Galois extension of function fields, if the Galois group satisfies a certain intersection property. For finite groups, this property is implied by having only elementary abelian Sylow p-subgroups. Note that such groups could be non-abelian. We show how the problem can be reduced to the totally wild ramified case on a p-extension. Our methodology is based on an intimate relationship between the ramification groups of the field extension and those of all degree p sub-extensions. Not only do we confirm that the Hasse-Arf property holds in this setting, but we also prove that the Hasse-Arf divisibility result is the best possible by explicit calculations of the quotients, which are expressed in terms of the different exponents of all those degree p sub-extensions.
dc.subjectFunction field extensions
dc.subjectRamification theory
dc.subject.lcshInverse Galois theory.
dc.subject.lcshFunctions, Abelian.
dc.subject.lcshAlgebraic functions.
dc.subject.lcshAlgebraic fields.
dc.titleThe Ramification Group Filtrations of Certain Function Field Extensions

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