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7 votes

Closed form roots for polynomial $x^9 + ax^6 + bx^5 + cx^3 + d = 0$

There is no way to transform your first polynomial to the special shape of the second polynomial while preserving its Galois group. The Galois group of the second polynomial is solvable, but for ...
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9 votes
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$N_{G}(E)/C_{G}(E)$ is the Weyl group of $G$?

$\newcommand{\ZZ}{{\mathcal Z}_G} \newcommand{\NN}{{\mathcal N}_G} \newcommand{\zz}{{\mathfrak z}_G} \newcommand{\Lie}{{\rm Lie\,}} \renewcommand{\tt}{{\mathfrak t}} \renewcommand{\gg}{{\mathfrak g}} \...
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5 votes
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Why does the category of abelian groups satisfy the axiom AB6?

The objects we are taking the limit over in the left side are $(i_j \in I_j)_j$, i.e. tuples of, for each $j\in J$, an element $i_j$ of $I_j$. These are the same as elements of $\prod_{j\in J}$. Thus, ...
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