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Results tagged with galois-theory
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user 5952
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
28
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1
answer
3k
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The Galois group of a random polynomial
Intuitively, the Galois group (of a splitting field over $\mathbb Q$ of) a polynomial $f\in\mathbb Q[X]$ taken at random is most probably the full permutation group on the roots of $f$. This intuition …
- 4,015
10
votes
2
answers
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What Dirichlet doesn't tell...
Let $n>1$ be an integer, and let us consider the set $P(n)$ of all prime numbers $p$ such that $p$ is not congruent to $1$ modulo $n$. Dirichlet's Density Theorem tells us that $P(n)$ has a natural de …
- 4,015
0
votes
Accepted
what is the first Galois cohomology group of the Galois module End(T_l(A)) for some abelian ...
In general, if $G$ is a profinite group and $M$ a continuous discrete $G$--module, then $H^i(G,M)$ is torsion for $i>0$. This applies in particular to Galois cohomology, i.e. when $G$ is a Galois grou …
- 4,015