On Rings of Invariants for Cyclic p-Groups
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On Rings of Invariants for Cyclic p-Groups
University of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupsrsity of Arkansas. FayettevilleFollow this and additional works at: https://scholarworks.uark.edu/etdỞ* Part of the Algebra CommonsCitationJuda. D. (2017). On Rings of Invariants for Cyclic p-Groups. Graduate Theses and Dissertations Retrieved from https://scholarworksuark.edu/etd/1981This Dissertat On Rings of Invariants for Cyclic p-Groupsion is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Graduate Theses and Dissertations by an autOn Rings of Invariants for Cyclic p-Groups
horized administrator of ScholarWorks@UARK. For more information, please contact scholar@uark.edu.On Rings of Invariants for Cyclic p-GroupsA dissertaUniversity of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupsersity Bachelor of Science in Mathematics. 2013 University of ArkansasMaster of Science in Mathematics. 2015May 2017 University of ArkansasThis dissertation is approved for recommendation to the Graduate Council.Dr. Lance E. MillerDissertation DirectorDr. Mark .Johnson Committee MemberDr. Paolo Mant On Rings of Invariants for Cyclic p-GroupscroCommittee MemberAbstractThis thesis studies the ring of invariants If’ of a cyclic //-group 6' acting on Ẩ:[;E1,... ,xn] whore k is a field of charOn Rings of Invariants for Cyclic p-Groups
acteristic p > 0. Wo consider when Ff: is Cohen-Macaulay and give an explicit, computation of the depth of ỉf;. Using representation theory and a resuUniversity of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupsational and when if’ Is 1- regular.Wo also study the (-/-invariant for a graded ring s, that is. the maximal graded degree of t he top local cohomology module of s. We give an upper bound for t he a invariant of ĩf: and wo show for any subgroup H < (7, wo can bound the (/-invariant of ĩf: by the a-i On Rings of Invariants for Cyclic p-Groupsnvariant of liH. We extend this result to more general modular rings of invariants where ỉf'ư is quasi-Gorenslein and G' has a normal, cyclic, p-SylowOn Rings of Invariants for Cyclic p-Groups
subgroup.Given a subgroup H < G wo consider the natural action of fl on ỈÌ and the associated ring of invariants ỈỈH. When G acts in a particular wayUniversity of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupscity of If: in a way that docs not depend on finding explicit generators for If’. We extend this result to modular rings of invariants for grou|)s G' which have a normal, cyclic, p-Sylow subgroup.Finally, we also consider computations of the norm of X.Ị for a cyclic modular action on ... ,xn]. This On Rings of Invariants for Cyclic p-Groupsbuilds on and extends work of Sczer and Shank.AcknowledgementsIwould first and foremost like to thank my mother and father, Susan and Paul, for alwaysOn Rings of Invariants for Cyclic p-Groups
being a source of inspiration and encouragement. I would also like to t hank my uncles, Richard Raymond and Michael .Juda, without whom my interest iUniversity of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupse.I would also like to thank my friends at. the University of Arkansas, and in particular William Taylor, Jesse Keyton, and Kevser Erdem, who have made the graduate experience exceptional and have helped me through all the moments of difficulty and frustration.1 want to recognize the professors at P On Rings of Invariants for Cyclic p-Groupsacific Lutheran University, and in particular Thomas Edgar, for giving me a solid grounding in mathemat ics t hat set me on t he pat h to success. 1 wOn Rings of Invariants for Cyclic p-Groups
ould like to recognize the math department staff at the University of Arkansas for their exceptional work helping me with this process..My committee hUniversity of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniver On Rings of Invariants for Cyclic p-Groupsd help.University of Arkansas, FayettevilleScholarWorks@UARKGraduate Theses and Dissertations42856On Rings of Invariants for Cyclic p-GroupsDaniel JudaUniverGọi ngay
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