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Hilbert's irreducibility theorem and its application to the inverse Galois problem
Dissertation (MSc (Mathematics))--University of Pretoria, 2005.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2013
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| _version_ | 1867613572055433216 |
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| access_status_str | Open Access |
| author2 | Pretorius, Lou M. (Lourens Martin) |
| author_browse | Pretorius, Lou M. (Lourens Martin) |
| author_facet | Pretorius, Lou M. (Lourens Martin) |
| collection | Thesis |
| dc_rights_str_mv | © 2005, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Mathematics))--University of Pretoria, 2005. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/31475 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:16.420Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/31475 Hilbert's irreducibility theorem and its application to the inverse Galois problem Pretorius, Lou M. (Lourens Martin) koffie@tuks.co.za Van Zyl, Jacobus Visser UCTD Hilbert's irreducibility theorem Galois extensions Inverse galois problem Number theory Galois theory Dissertation (MSc (Mathematics))--University of Pretoria, 2005. To every polynomial f (x) with rational coefficients one can associate a finite group Gf , the Galois group of the splitting field of f over the rational numbers. The inverse problem of Galois theory asks whether for a given finite group G, there exists a polynomial f such that G is isomorphic to Gf. A Galois extension of Q, with Galois group G, is called a realisation of G over Q, and G is said to occur over Q. It is known that all abelian groups occur over Q, and Šafereviè showed in 1957 that all solvable groups occur over Q. Almost all other progress with the problem depends on Hilbert’s irreducibility theorem, which implies that a realisation of G over Q exists if and only if a realisation exists over the function field Q (x). Hence it suffices to find realisations of a particular group G over Q (x), which enables us to use tools from Riemannian Surface Theory and Algebraic Geometry. Mathematics and Applied Mathematics Restricted Natural and Agricultural Sciences 2013-09-09T12:18:18Z 2006-05-15 2013-09-09T12:18:18Z 2005-11-30 2005 2005-12-07 Dissertation Van Zyl, J 2005, Hilbert's irreducibility theorem and its application to the inverse Galois problem, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-12072005-121619/ > http://hdl.handle.net/2263/31475 http://upetd.up.ac.za/thesis/available/etd-12072005-121619/ en © 2005, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Hilbert's irreducibility theorem Galois extensions Inverse galois problem Number theory Galois theory Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title | Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title_full | Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title_fullStr | Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title_full_unstemmed | Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title_short | Hilbert's irreducibility theorem and its application to the inverse Galois problem |
| title_sort | hilbert s irreducibility theorem and its application to the inverse galois problem |
| topic | UCTD Hilbert's irreducibility theorem Galois extensions Inverse galois problem Number theory Galois theory |
| url | http://hdl.handle.net/2263/31475 http://upetd.up.ac.za/thesis/available/etd-12072005-121619/ |