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arXiv · 0809.2166

On the descending central sequence of absolute Galois groups

Ido Efrat·Jan Minac
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Abstract

Let $p$ be an odd prime number and $F$ a field containing a primitive $p$th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group $G_F$ of $F$. Namely, the third subgroup $G_F^{(3)}$ in the descending $p$-central sequence of $G_F$ is the intersection of all open normal subgroups $N$ such that $G_F/N$ is 1, $\mathbb{Z}/p^2$, or the modular group $M_{p^3}$ of order $p^3$.

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Ido Efrat, Jan Minac. 2008-09-12. On the descending central sequence of absolute Galois groups. https://arxiv.org/abs/0809.2166

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