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
http://www.math-atlas.org/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!