Tagged Questions
22
votes
1answer
255 views
Is the Galois group associated to a random polynomial solvable with probability 0?
Choose a random polynomial $P\in\mathbb{Z}[x]$ of degree $n$ and coefficients $\leq n$ and $\geq-n$.
Let $r_1,\ldots,r_n$ be the roots of $P$ and consider ...
1
vote
1answer
77 views
What is the galois group of $x+3$ or $(x+1)(x+2)$ ? How about $A(x)B(x)$?
As the title says I wonder what the galois group of $x+3$ is.
Or even if that exists ? Since $x+3 = 0$ has only one zero/element I assume its the trivial group ? And what is the galois group of ...
3
votes
2answers
181 views
An explicit calculation of Galois group
This is a question requires to compute the Galois group of $X^4+1$ over $\mathbb{Q}$, $\mathbb{Q}(i)$, $\mathbb{F}_3$ and $\mathbb{F}_5$.
Here is a brief of what I can think of.
For the first two, ...
4
votes
2answers
200 views
$p$-Sylow subgroups of a group of order $5^3\cdot 29^2$
I need to calculate the $p$-Sylow subgroups of a Galois group with order $5^3 \cdot 29^2$, i.e. $|\mathrm{Gal}(K/F)|=5^3 \cdot 29^2$.
I've already established that there is only one 29-Sylow-subgroup ...
