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The inverse Galois problem

Tiesinga, H.G.J. (2016) The inverse Galois problem. Bachelor's Thesis, Mathematics.

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Abstract

Some specific field extensions L|K are classified as Galois extensions. We call the group of automorphisms of such L|K the Galois group of L|K. The inverse Galois problem asks the question whether every finite group is isomorphic to the Galois group of a Galois extension of the rational numbers. We describe the known solutions of this problem for abelian groups, for the symmetric groups S_n and for the alternating groups A_n and even establish specific Galois extensions for the latter two. We conclude with a description of a way to establish some semidirect products as Galois groups.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:14
Last Modified: 15 Feb 2018 08:14
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/14148

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