Galois group


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Galois group

[′gal‚wä ‚grüp]
(mathematics)
A group of isomorphisms of a particular field extension associated with a polynomial's roots.
References in periodicals archive ?
Their cohomology carries actions both of a linear algebraic group (such as gln) and a galois group associated with the number field one is studying.
As one can see, Theorem 3 implies that the Galois group [G.
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].
Hilbert's Theorem 90) Let F' be a finite extension of F whose Galois group G is cyclic generated by [sigma].
1 by examining the Galois group of a suitable extension of Q(i).
n] is the Galois group of some subspace in the k-equal arrangement.
Frohlich, On the absolute Galois group of abelian fields, J London Math.
v] is a Galois extension with its Galois group [[GAMMA].
x] be the multiplicative group, which we naturally identify with the Galois group Gal(Q([[zeta].
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 of k.
infinity]] the unique abelian extension of Q in C whose Galois group over Q is topologically isomorphic to the additive group of Z/.