Groups with the same cohomology as their pro-p completions
| Autor: | Karl Lorensen |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Class (set theory) Algebra and Number Theory 20JO6 20E18 20E06 20F36 Group (mathematics) Prime number Natural number K-Theory and Homology (math.KT) Group Theory (math.GR) Cohomology Prime (order theory) Free product Mathematics - K-Theory and Homology FOS: Mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. (1):6-14 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2009.04.002 |
| 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. 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: | OpenAIRE |
| Externí odkaz: |
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