Groups with the same cohomology as their pro-p completions

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 1 2010

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Completion
Cohomology
Free Product with Amalgamation
Right-angled Artin Group
Prime number
Natural number
Trivial
Denote
Module
Class

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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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.",
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Groups with the same cohomology as their pro-p completions. / Lorensen, Karl.

In: Journal of Pure and Applied Algebra, Vol. 214, No. 1, 01.01.2010, p. 6-14.

Research output: Contribution to journalArticle

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