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Galois group

   Also found in: Wikipedia 0.01 sec.
Galois group [′gal‚wä ‚grüp]
(mathematics)
A group of isomorphisms of a particular field extension associated with a polynomial's roots.


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She continues with action-angle variables, integrability and Galois groups (including the Arnold-Liouville theorem, as revisited through differentia Galois theory), Lax closing with an introduction to Lax equations as they apply to the Arnold-Liouville theorem.
With examples, exercises and open problems he covers examples low degree, nilpotent and solvable groups as Galois groups over Q, Hilbert's irreducibility theorem, Galois extensions of Q(T), Galois extensions of Q(T) given by torsion on elliptic curves, Galois extensions of C(T), rigidity and rationality on finite groups, construction of Galois extensions of Q(T) by the rigidity methods, the quadratic form and its applications, and in an appendix, the large sieve inequality.
On this basis rests the subsequent discussion of polynomials and their Galois groups and representations of the Galois group, followed by the reciprocity laws, including the famous proof by Andrew Wiles of Fermat's Last Theorem.
 
 
 
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