Groups with the same cohomology as their pro-$p$ completions
| Autor: | Lorensen, Karl |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | J. Pure Appl. Algebra 214 (2010), 6-14 |
| Druh dokumentu: | Working Paper |
| Popis: | For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\hat{G}^p$. Let $\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\hat{G^p},\mathbb Z/p)\cong H^n(G, \mathbb Z/p)$, where $\mathbb Z/p$ is viewed as a discrete, trivial $\hat{G}^p$-module. In this article we identify certain kinds of groups that lie in $\mathcal{C}$. In particular, we show that right-angled Artin groups are in $\mathcal{C}$ and that this class also contains some special types of free products with amalgamation. Comment: The revisions in the second version pertain to the exposition: the proof of Prop. 1.1, in particular, now includes more details. The third version includes a proof that right-angled Artin groups are residually $p$-finite for every prime $p$ |
| Databáze: | arXiv |
| Externí odkaz: |
|