Galois groups and monic polynomials in Z[x] of degrees at most 6

Zhang, Jiayi (2020) Galois groups and monic polynomials in Z[x] of degrees at most 6. Bachelor's Thesis, Mathematics.

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Abstract

In this bachelor's project, I aim to describe, given a general monic polynomial with integer coefficients of degrees at most 6, the Galois group of its splitting field over Q. First of all, there are two situations to consider: the polynomial is irreducible or reducible. In the former case, we can use discriminant, resolvent and the subtle connection between irreducibility and transitive subgroups of Sn; in the latter case, we can factor the polynomial into irreducible factors of smaller degrees, explore the relation among their splitting fields and apply the results we already obtained.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Top, J.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	13 Jul 2020 13:19
Last Modified:	13 Jul 2020 13:19
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/22609

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