On the descending central sequence of absolute Galois groups

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 $p^3$.

💡 Research Summary

The paper investigates the structure of the absolute Galois group (G_F) of a field (F) that contains a primitive (p)‑th root of unity, where (p) is an odd prime. The main object of study is the descending (p)-central series \