Hello


Suppose given a polynomial $P=Q\_1\cdots Q\_k$ of degree $n$, where each $Q\_i$ is irreducible. Suppose also that I know the Galois group $G\_i$ (over the rationals) of each irreducible factor $Q\_i$.


Is there an easy correlation between the Galois group of $P$, and the $G\_i$?



Galois group of a product of irreducible polynomials
The Galois group of $P$ will be a subdirect product of
the $G\_i$, that is a subgroup of $G\_1\times\cdots\times G\_k$
projecting surjectively onto each of the $G\_i$.


