Computation of polynomials generating abelian and GL(2, Fp) extensions of Q

Letina, Katrina (2024) Computation of polynomials generating abelian and GL(2, Fp) extensions of Q. Bachelor's Thesis, Mathematics.

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Abstract

The Inverse Galois problem asks whether any finite group G appears as the Galois group of some Galois extension L/Q. In this paper, we begin by proving that any finite abelian group appears as the Galois group of some intermediate field of a cyclotomic extension of Q. Additionally, using elliptic curves and their p-torsion points, we prove this result for the groups GL(2, Fp) as well. Lastly, we provide the necessary methods to compute polynomials in Q[X] generating these extensions.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Keller, T. and Top, J. and Muller, J.S.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	24 Jul 2024 14:24
Last Modified:	24 Jul 2024 14:24
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/33647

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