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Ramification in The Inverse Galois Problem / Benjamin Pollak.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Pollak, Benjamin, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Genre:
- Academic theses.
- Physical Description:
- 1 online resource (83 pages)
- Contained In:
- Dissertations Abstracts International 81-02B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2019.
- Language Note:
- English
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- This thesis focuses on a refinement of the inverse Galois problem. We explore what finite groups appear as the Galois group of an extension of the rational numbers in which only a predetermined set of primes may ramify. After presenting new results regarding extensions in which only a single finite prime ramifies, we move on to studying the more complex situation in which multiple primes from a finite set of arbitrary size may ramify. We then continue by examining a conjecture of Harbater that the minimal number of generators of the Galois group of a tame, Galois extension of the rational numbers is bounded above by the sum of a constant and the logarithm of the product of the ramified primes. We prove the validity of Harbater's conjecture in a number of cases, including the situation where we restrict our attention to finite groups containing a nilpotent subgroup of index 1, 2 or 3, and also derive consequences that are implied by the truth of this conjecture. We conclude by exploring how circumstances change when the base field of the rational numbers is replaced by an arbitrary number field.
- Notes:
- Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
- Advisors: Harbater, David; Committee members: Florian Pop; Mona Merling.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2019.
- Local Notes:
- School code: 0175
- ISBN:
- 9781085626002
- Access Restriction:
- Restricted for use by site license.
- This item must not be sold to any third party vendors.
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