All Questions

We reprint an old math SE question here (see https://math.stackexchange.com/questions/1241224/composition-of-polynomials-and-galois-theory): " Let $f(x)$ be a polynomial of degree $n$ over $\...

The inverse Galois problem asks whether every finite group appears as the Galois group of a Galois extension of the rational numbers. Is anything known about the anologous problem, where the ...

Given two positive integers $n,m$, which positive integers $d$ appear as the degree of $\mathbb{Q}(a,b)$ for two algebraic numbers $a$ and $b$ of degrees $n$ resp. $m$? Two necessary conditions are $\...

Let $F$ be a infinite field of characteristic 2 whose multiplicative group $F^*$ is torsion free. I would like to conclude that $F^*$ is decomposable or find an example where $F^*$ is indecomposable. ...

I always wondered if the fact that the quartic can be solved by a cubic can be generalized to other even degrees $n$, namely if there is an ordering of the roots $x_i$ of form $x_1x_2+x_3x_4+\dots+x_{...