## Finding the isomorphism class of a Galois Group [closed]

Let $F = C(T), R = C[T]$ ie, $F$ is the fraction field of the ring, $R$. $C$ is the complex numbers. Let p be prime.

Let $y$ be a non-trivial p-th root of unity. Choose $a$ and $b$ in the algebraic closure of $F$ such that $ap = T$ and $bp = (1-T)$. Let $E = F(a,b)$ e.x joining the binary set of roots to the field.

How do you determine the isomorphism class of the Galois group of $E/F$?

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 What do you mean by "C is a set of the complex numbers" ? Is C "the" set of complex numbers, or "a" subset of the complex numbers ? – TJ Oct 19 2011 at 23:11 Sorry for the ambiguity, C is the complex numbers. – Zephyr Pellerin Oct 20 2011 at 1:12 Where does $y$ come in? And why are $a$ and $b$ not already in $F$? – Steve D Oct 20 2011 at 1:41 Wild guess: You really want to consider $p$th roots of $T$ and $1-T$, rather than dividing the polynomials by roots of unity. This makes the answer non-trivial (in fact of order $p^2$). I suggest you ask this question at math.stackexchange.com or one of the other sites listed in the FAQ. – S. Carnahan♦ Oct 20 2011 at 1:56