The group [G.sub.P] = Gal(C(C)/[K.sub.P]) is called the Galois group
The main result of this theory merely says that if a Hamiltonian system is completely integrable, then the identity component of the Galois group
of the variational equation along certain particular solution is abelian.
If K [??] E is a finite Galois field extension and G is its Galois group
, then the opposite category of K-algebras A with E [[cross product].sub.K] A [approximately equal to] [E.sup.n] for some natural n is equivalent to the category of finite G-sets.
Conversely, every irreducible parabolic subgroup of rank k - 1 in [A.sub.n] is the Galois group
of some subspace in the k-equal arrangement.
The aim of this paper is to study the Galois group
of a certain factor of a 4-th dynatomic polynomial.
First of all, [S.sub.n] is canonically a profinite group, and Gal [equivalent to] Gal([F.sub.[p.sup.n]]/[F.sub.p]), the Galois group
of automorphisms of [F.sub.[p.sup.n]], acts continuously in an evident way on [S.sub.n].
then the Galois group
[G.sub.P] of the splitting field of P(x) over Q is of order at most 132.
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.
All of the examples are division algebra representatives of algebras of the form A [cross product] [delta]([chi]), where A is a k-division algebra and [delta]([chi]) is the cyclic k(t) or k((t))-division algebra defined by a character [chi] of the absolute Galois group