The lower $p$-central series of a free profinite group and the shuffle algebra

Ido Efrat

For a prime number $p$ and a free profinite group $S$ on the basis $X$, let $S^{(n,p)}$, $n=1,2,\dots$ be the lower $p$-central filtration of $S$. For $p>n$, we give a combinatori…