All Questions

Let $\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]] := \varprojlim_{n,m}(\mathbb{Z}/n)[x]/(x^m-1)$ be the complete group algebra of the profinite free group of rank 1. In Corollary 5.9.2 of Ribes-...

Let $G$ be a group, and let $\mathbb{Z}[G]$ denote its group ring. Its profinite completion is the inverse limit over all ideals of finite index. By Benjamin Steinberg's answer here, this profinite ...

Is there an absolute Galois group that is not a subgroup of $\hat{\mathbb{Z}}$ and that has one and only one closed non-open subgroup?

Let $\mathbb{Z}_p$ the ring of $p$-adic numbers. It's known that the multiplicative unit group $\mathbb{Z}_p ^\times$ can be set theoretically described as $\bigcup _{1 \le a \le p-1} a+ p\mathbb{Z}_p$...

This is a pretty basic question, but I suspect it might be too exotic for math.stackexchange. Let $\mathbb{Z}_p$ be the $p$-adic integers. For free pro-$p$ group $F_r$ of rank $r$, we can consider ...