From: rusin@vesuvius.math.niu.edu (Dave Rusin) Subject: Re: Inverse Galois Theory? Date: 17 Oct 1999 22:31:36 GMT Newsgroups: sci.math In article <7ua8sn$tqe$1@news.postech.ac.kr>, Ì¿ëÇÐ wrote: >I seek for the reference about 'Inverse Galois Theory'.. Well, the "Inverse Galois Problem" is the question, is every finite group the Galois group of some polynomial? It's known that every solvable group occurs (From memory that was Shafarevich? ca. 1950?) and a host of simple and other non-solvable examples have also been studied. More generally, the right question is, what are the finite quotients of the absolute Galois group Gal(Kbar/K) where Kbar is the algebraic closure of K. When K = Q this is the same question as in the previous paragraph, but it's a reasonable question for, say, number fields, finite fields, etc. Of course it's no longer an "inverse" problem when you look at it this way -- you're just asking for a really good description of a single Galois group, albeit an infinite one :-) A recent survey article is Debes, Pierre; Deschamps, Bruno The regular inverse Galois problem over large fields. Geometric Galois actions, 2, 119--138, London Math. Soc. Lecture Note Ser., 243, Cambridge Univ. Press, Cambridge, 1997 MR99j:12002 and as you might imagine, there's plenty of information in Recent developments in the inverse Galois problem (Seattle, WA, 1993), Contemp. Math., 186, Amer. Math. Soc., Providence, RI, 1995. For Galois theory more generally you might want to look at index/12FXX.html dave ============================================================================== From: t Subject: Re: Inverse Galois Theory? Date: Mon, 18 Oct 1999 00:20:28 GMT Newsgroups: sci.math There is an excellent monograph by Jean-Pierre Serre called "Topics in Galois Theory" based on a course given by him at Harvard focused mainly on the inverse Galois problem. It is published by Jones and Bartlett publishers in their Research Notes in Mathematics series (Vol. 1). isbn 0-86720-210-6. There is also a workshop proceedings from MSRI in Berkeley by Y. Ihara, K. Ribet and J.-P. Serre called "Galois Groups over Q", published by Springer isbn0-387-97031-2. Hope this helps, Regards, t "ÀÌ¿ëÇÐ" wrote: > I seek for the reference about 'Inverse Galois Theory'.. > If you know about it, please let me know about that subject.. :) > My e-mail address is rayden@postech.ac.kr. > please e-mail to me~ thank you!