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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