Groups with the same cohomology as their pro-p completions

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Abstract

For any prime p and group G, denote the pro-p completion of G by over(G, ̂)p. Let C be the class of all groups G such that, for each natural number n and prime number p, Hn (over(Gp, ̂), Z / p) ≅ Hn (G, Z / p), where Z / p is viewed as a discrete, trivial over(G, ̂)p-module. In this article we identify certain kinds of groups that lie in C. In particular, we show that right-angled Artin groups are in C and that this class also contains some special types of free products with amalgamation.

Original languageEnglish (US)
Pages (from-to)6-14
Number of pages9
JournalJournal of Pure and Applied Algebra
Volume214
Issue number1
DOIs
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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