Find out how to access previewonly content
Volume 174 of the series Lecture Notes in Computer Science pp 225236
Date:
Polynomial time algorithms for Galois groups
 Susan LandauAffiliated withMath Department, Wesleyan University
Abstract
In this paper we present several polynomial time algorithms for Galois groups. We show:
 (i)
There are polynomial time algorithms to determine:
 (a)
If the Galois group of an irreducible polynomial over Q is a pgroup.
 (b)
the prime divisors of the order of a solvable Galois group
 (ii)
Using the classification theorem for finite simple groups, there is a polynomial time algorithm to determine whether an irreducible polynomial over Q has Galois group S_{n} or A_{n}.
We consider several techniques for computing Galois groups, including the Chebatorev Density Theorem, and their applicability to polynomial time computations.
 Title
 Polynomial time algorithms for Galois groups
 Book Title
 EUROSAM 84
 Book Subtitle
 International Symposium on Symbolic and Algebraic Computation Cambridge, England, July 9–11, 1984
 Pages
 pp 225236
 Copyright
 1984
 DOI
 10.1007/BFb0032845
 Print ISBN
 9783540133506
 Online ISBN
 9783540388937
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 174
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Authors

 Susan Landau ^{(1)}
 Author Affiliations

 1. Math Department, Wesleyan University, 06457, Middletown, CT.
Continue reading...
To view the rest of this content please follow the download PDF link above.