Groups with the same cohomology as their profinite completions

Karl Lorensen

doi:10.1016/j.jalgebra.2008.03.013

Groups with the same cohomology as their profinite completions

Karl Lorensen

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

For any positive integer n, A_n is the class of all groups G such that, for 0 ≤ i ≤ n, Hⁱ (over(G, ̂), A) ≅ Hⁱ (G, A) for every finite discrete over(G, ̂)-module A. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes A_n. In addition, we investigate the residually finite groups in the class A₂.

Original language	English (US)
Pages (from-to)	1704-1722
Number of pages	19
Journal	Journal of Algebra
Volume	320
Issue number	4
DOIs	https://doi.org/10.1016/j.jalgebra.2008.03.013
State	Published - Aug 15 2008

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2008.03.013

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title = "Groups with the same cohomology as their profinite completions",

abstract = "For any positive integer n, An is the class of all groups G such that, for 0 ≤ i ≤ n, Hi (over(G,{\^ }), A) ≅ Hi (G, A) for every finite discrete over(G,{\^ })-module A. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes An. In addition, we investigate the residually finite groups in the class A2.",

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AB - For any positive integer n, An is the class of all groups G such that, for 0 ≤ i ≤ n, Hi (over(G, ̂), A) ≅ Hi (G, A) for every finite discrete over(G, ̂)-module A. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes An. In addition, we investigate the residually finite groups in the class A2.

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DO - 10.1016/j.jalgebra.2008.03.013

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SP - 1704

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 4

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Groups with the same cohomology as their profinite completions

Abstract

All Science Journal Classification (ASJC) codes

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