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	Inverse Galois problem - Wikipedia, the free encyclopedia
		In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q.
		This problem, first posed by Emmy Noether, is unsolved.
		Some of this is based on constructing G geometrically as a Galois covering of the projective line: in algebraic terms, start with an extension of the field Q(t) of rational functions in an indeterminate t.
	en.wikipedia.org /wiki/Inverse_Galois_problem (635 words)

	Encyclopedia :: encyclopedia : Galois theory (Site not responding. Last check: 2007-10-23)
		In mathematics, Galois theory is a branch of abstract algebra.
		Galois theory not only provides a beautiful answer to this question, it also explains in detail why it is possible to solve equations of degree four or lower in the above manner, and why their solutions take the form that they do.
		The central idea of Galois theory is to consider those permutations (or rearrangements) of the roots having the property that any algebraic equation satisfied by the roots is still satisfied after the roots have been permuted.
	www.hallencyclopedia.com /Galois_theory (1569 words)

	Galois theory
		In mathematics, Galois theory is that branch of abstract algebra which studies the symmetries of the roots of polynomial s.
		Symmetries are usually expressed in terms of symmetry group s, and in fact the very notion of a group was invented by Evariste Galois to describe symmetries of roots.
		This is called the inverse Galois problem, and is usually posed for extensions of the rational number field 'Q'''.
	www.nebulasearch.com /encyclopedia/article/Galois_theory.html (949 words)

	Inverse Galois Theory (Springer Monographs in Mathematics)
		Kurzbeschreibung Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field.
		In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory.
		Synopsis Inverse Galois theory is concerned with the question of which finite groups occur as Galois Groups over a given field.
	www.uni-protokolle.de /buecher/isbn/3540628908 (243 words)

	UF Mathematics: About Group Theory
		When Galois investigated the solvability of polynomial equations in terms of radicals, he studied certain types of groups associated with such equations which are called Galois groups today.
		The Inverse Galois Problem concerns the question whether for any given group there exists a polynomial equation such that the Galois group associated with the solution of this equation is the given group.
		A famous problem that remained unsolved for many years was the conjecture that every group with an odd number of elements is solvable.
	www.math.ufl.edu /dept_news_events/honors/group_theory.html (530 words)

	Amazon.com: Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Mathematical Sciences Research ... (Site not responding. Last check: 2007-10-23)
		The main theme is an exposition of a family of "generic" polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group.
		The book also introduces the notion of "generic dimension" to address the problem of the smallest number of parameters required by a generic polynomial.
		Introduces the notion of generic dimension to address the problem of the smallest number of parameters required by a generic polynomial.
	www.amazon.com /exec/obidos/tg/detail/-/0521819989?v=glance (760 words)

	Publications of the SPACES team
		In order to simplify the problem, we use strongly the fact that a manipulator cannot be constructed with exact parameters, in other words, we are just interested in the generic solutions of our problem.
		However, some specific symbolic computation problems have received in the last years new algorithmic solutions, which enabled to push further the limits of what is doable within a reasonable amount of time and space.
		Such algorithms are useful, as they occur in several problems, such as the Toom-Cook-like algorithms to multiply large multiple-precision integers, the approximate computation of consecutive values of a polynomial, and the generation of integer multiplications by compilers.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Galois Theory (Site not responding. Last check: 2007-10-23)
		Galois theory is one of the jewels of mathematics.
		This undergraduate text develops the basic results of Galois theory, with Historical Notes to explain how the concepts evolved and Mathematical Notes to highlight the many ideas encountered in the study of this marvelous subject.
		Section 13.2 discusses how to compute the Galois group of a quintic polynomial and in Example 13.2.13 mentions the problem of finding the roots of a quintic that is solvable by radicals.
	www.cs.amherst.edu /~dac/galois.html (461 words)

	Applying Modular Towers to the Inverse Galois Problem - Fried, Kopeliovic (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Abstract: Let G be a finite (possibly simple) group, and let p be a prime dividing the order of G. The characteristic finite quotients k p ~ G of the universal p-Frattini cover of G are strikingly similar groups.
		M.D. Fried and Y. Kopeliovic, Applying modular towers to the inverse Galois problem, Geometric Galois Actions II Dessins d'Enfants, Mapping Class Groups and Moduli, vol.
		13 The inverse Galois problem and rational points on moduli spa..
	citeseer.ist.psu.edu /473877.html (470 words)

	Amazon.com: Groups as Galois Groups: An Introduction (Cambridge Studies in Advanced Mathematics): Books: Helmut ... (Site not responding. Last check: 2007-10-23)
		This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century.
		The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realization of groups as Galois groups.
		Galois Groups over Q: Proceedings of a Workshop Held March 23-27, 1987 (Mathematical Sciences Research Institute Publications) by Y. Ihara in Back Matter
	www.amazon.com /exec/obidos/tg/detail/-/0521562805?v=glance (648 words)

	Number Theory (Site not responding. Last check: 2007-10-23)
		The inverse Galois problem for p-adic Lie algebras
		For a number field K and a (compact) p-adic Lie groups G, the inverse Galois problem asks whether G can be realized as the Galois group of an extension of K. Already in the case that G is zero-dimensional, this is too difficult.
		So I propose to relax the problem and ask which p-adic Lie algebras can be realized.
	www.math.princeton.edu /~seminar/2004-05-sem/LarsenAbstract4-15-2005 (67 words)

	#45: Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Site not responding. Last check: 2007-10-23)
		This book describes a constructive approach to the inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G.
		Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G.
		The main theme of the book is an exposition of a family of “generic” polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group.
	www.msri.org /communications/books/Book45/desc.html (163 words)

	Hilbert's irreducibility theorem - Wikipedia, the free encyclopedia
		More formally, writing P(X, Y) for the polynomial, there will be infinitely many choices of a rational number q, such that
		This result has applications, in particular, to the inverse Galois problem.
		It is also used as a step in the Andrew Wiles proof of Fermat's last theorem.
	en.wikipedia.org /wiki/Hilbert's_irreducibility_theorem (147 words)

	Amazon.ca: Recent Developments in the Inverse Galois Problem: A Joint Summer Research Conference on Recent Developments ... (Site not responding. Last check: 2007-10-23)
		Amazon.ca: Recent Developments in the Inverse Galois Problem: A Joint Summer Research Conference on Recent Developments in the Inverse Galols Problem July 17-23, 1993 : University of Washington, Seattle: Books
		Recent Developments in the Inverse Galois Problem: A Joint Summer Research Conference on Recent Developments in the Inverse Galols Problem July 17-23, 1993 : University of Washington, Seattle
		Top of Page : Recent Developments in the Inverse Galois Problem: A Joint Summer Research Conference on Recent Developments in the Inverse Galols Problem July 17-23, 1993 : University of Washington, Seattle
	www.amazon.ca /exec/obidos/ASIN/0821802992 (301 words)

	Katz' Existence Algorithm and its Application to the Inverse Galois Problem (Site not responding. Last check: 2007-10-23)
		Katz' Existence Algorithm and its Application to the Inverse Galois Problem
		This functor commutes with the braiding group action on tuples of matrices.
		This yields a new approach in inverse Galois theory for realizing subgroups of linear groups regularly as Galois groups over Q.
	www.math.jussieu.fr /projets/tn/STN/01/resume-Reiter.html (113 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Applying modular towers to the Inverse Galois Problem
		In this paper we apply Modular towers to the Inverse Galois Problem and the main conjecture is formulated which states roughly that there do not exist projective limits of rational points on the Modular towers.
		First steps towards attacking this conjecture are taken and its implication to the Inverse Galois problem is described.
	www.math.fsu.edu /~aluffi/archive/paper52.abs.html (61 words)

	Citebase - On the Constructive Inverse Problem in Differential Galois Theory (Site not responding. Last check: 2007-10-23)
		Citebase - On the Constructive Inverse Problem in Differential Galois Theory
		On the Constructive Inverse Problem in Differential Galois Theory
		Authors: Cook, William J. Mitschi, Claude; Singer, Michael F. We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0403378 (101 words)

	Applying Modular Towers to the Inverse Galois Problem - Fried, Kopeliovic (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Please let us know if you encounter any data corruptions.
		If it holds, then you cannot realize all G k s with a bounded number of branch points.
		1.8: Variables Separated Polynomials, The Genus 0 Problem And Moduli..
	citeseer.ist.psu.edu /370443.html (535 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		A generic Approach to the Inverse Differential Galois Problem, Part I
		In conclusion we are going to give a short proof of the Evanovich's result.
		A generic Approach to the Inverse Differential Galois Problem, Part II
	math.hunter.cuny.edu /ksda/2003-04/nov03.htm (176 words)

	Amazon.ca: Generic Polynomials : Constructive Aspects of the Inverse Galois Problem: Books (Site not responding. Last check: 2007-10-23)
		You can view sample pages from this book.
		Be the first person to review this item.
		Top of Page : Generic Polynomials : Constructive Aspects of the Inverse Galois Problem
	www.amazon.ca /exec/obidos/ASIN/0521819989 (378 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Yaacov Kopeliovich (Florida State University) Topic: Modular towers and the Inverse Galois Problem Date: Thursday, December 26, 1996 Place: Room 1420 of the Eshkol Tower Building, Haifa University.
		Time: 10:30 AM (Tea at 10:00 AM) ABSTRACT Modular towers were introduced by M. Fried to deal in a very broad sense with an Inverse Galois Problem.
		In this talk we will explain the construction, which uses Frattini covers of finite groups, and then indicate some results of our joint work.
	www.math.technion.ac.il /~techm/oldmessages/2257 (102 words)

	Mathematica in Abstract Algebra: The Inverse Galois Problem -- from Mathematica Information Center
		Mathematica in Abstract Algebra: The Inverse Galois Problem -- from Mathematica Information Center
		Mathematica in Abstract Algebra: The Inverse Galois Problem
		The interrelatedness of topics in an abstract algebra course are revealed through the exploration of an open question.
	library.wolfram.com /infocenter/Articles/2734 (39 words)

	Talks
		A generic approach to the inverse differential Galois problem
		The generic inverse differential Galois problem for linear algebraic groups
		On the inverse differential Galois Problem for GLn
	www.math.ttu.edu /~ljuan/lects.html (619 words)

	Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups; Paperback
		Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups; Paperback
		Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups
		Prices subject to change to be advised on confirmation of order.
	www.netstoreusa.com /mabooks/052/0521596416.shtml (189 words)

	Find in a Library: Generic polynomials : constructive aspects of the inverse Galois problem
		Find in a Library: Generic polynomials : constructive aspects of the inverse Galois problem
		Generic polynomials : constructive aspects of the inverse Galois problem
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	worldcatlibraries.org /wcpa/ow/0d19374da3350a37a19afeb4da09e526.html (77 words)

	Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Site not responding. Last check: 2007-10-23)
		You may also be able to place a request for this book via these links: Buy.com, Books-A-Million, and Overstock.com
		Book Description: This book describes a constructive approach to the Inverse Galois problem.
		Contact them for corrections and licensing, or read more about our data.
	isbn.nu /0521819989 (393 words)

	Citebase - On a generic inverse differential Galois problem for GLn (Site not responding. Last check: 2007-10-23)
		Citebase - On a generic inverse differential Galois problem for GLn
		On a generic inverse differential Galois problem for GL n
		If E⊃ F is any Picard-Vessiot extension with differential Galois group GL then E≅ F(X
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0012063 (175 words)

	Generic Polynomials -- Constructive Aspects of the Inverse Galois Problem -- Christian U. Jensen Arne Ledet Norkio Yui
		Generic Polynomials -- Constructive Aspects of the Inverse Galois Problem -- Christian U. Jensen Arne Ledet Norkio Yui
		Click Here to tell a friend about this book
		The number of parameters; Appendix A. Technical results; Appendix B. Invariant theory; Bibliography; Index.
	www.frontlist.com /detail/0521819989 (135 words)

	Table of contents for Library of Congress control number 2002067674
		Table of contents for Generic polynomials : constructive aspects of the inverse Galois problem / Christian U. Jensen, Arne Ledet, Noriko Yui.
		Bibliographic record and links to related information available from the Library of Congress catalog
		Library of Congress subject headings for this publication: Inverse Galois theory, Polynomials
	www.loc.gov /catdir/toc/cam031/2002067674.html (80 words)

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