Publication Date
1-9-2018
Document Type
Thesis
Degree Name
Master of Science in Mathematics (MS)
Committee Chair
Wu, Qingquan
Committee Member
Khasawneh, Mahmoud
Committee Member
Lin, Runchang
Committee Member
Milovich, David
Abstract
We 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.
Recommended Citation
Castaneda, Jeffrey Anthony, "The Ramification Group Filtrations of Certain Function Field Extensions" (2018). Theses and Dissertations. 91.
https://rio.tamiu.edu/etds/91
