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Corrigendum to “Groups with the same cohomology as their profinite completions” [J. Algebra 320 (2008) 1704–1722]
Journal of Algebra 321 (2009) 741
Contents lists available at ScienceDirect
Journal of Algebra www.elsevier.com/locate/jalgebra
Corrigendum
Corrigendum to “Groups with the same cohomology as their profinite completions” [J. Algebra 320 (2008) 1704–1722] Karl Lorensen Mathematics Department, Pennsylvania State University, Altoona College, 3000 Ivyside Park, Altoona, PA 16601-3760, USA
a r t i c l e
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Article history: Received 17 October 2008 Available online 8 November 2008
The definition given of right-angled Artin groups in the above paper is incorrect; it should read as follows. Definition. A right-angled Artin group is any group with a finite generating set X and a presentation of the form
X [x, y ] = 1 for all (x, y ) ∈ Σ for some subset Σ of the Cartesian product X × X . The proofs of the results concerning right-angled Artin groups contained in the article are all based on the correct definition, not the erroneous one that appears in the paper. We also take this opportunity to remedy an omission in the proof of Theorem 3.4, where the symbol G is employed without identifying what G represents. In terms of the notation in the theorem, G is supposed to be G 1 ∗ N G 2 .
DOI of original article: 10.1016/j.jalgebra.2008.03.013. E-mail address: [email protected]. 0021-8693/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2008.10.014
Contents lists available at ScienceDirect
Journal of Algebra www.elsevier.com/locate/jalgebra
Corrigendum
Corrigendum to “Groups with the same cohomology as their profinite completions” [J. Algebra 320 (2008) 1704–1722] Karl Lorensen Mathematics Department, Pennsylvania State University, Altoona College, 3000 Ivyside Park, Altoona, PA 16601-3760, USA
a r t i c l e
i n f o
Article history: Received 17 October 2008 Available online 8 November 2008
The definition given of right-angled Artin groups in the above paper is incorrect; it should read as follows. Definition. A right-angled Artin group is any group with a finite generating set X and a presentation of the form
X [x, y ] = 1 for all (x, y ) ∈ Σ for some subset Σ of the Cartesian product X × X . The proofs of the results concerning right-angled Artin groups contained in the article are all based on the correct definition, not the erroneous one that appears in the paper. We also take this opportunity to remedy an omission in the proof of Theorem 3.4, where the symbol G is employed without identifying what G represents. In terms of the notation in the theorem, G is supposed to be G 1 ∗ N G 2 .
DOI of original article: 10.1016/j.jalgebra.2008.03.013. E-mail address: [email protected]. 0021-8693/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2008.10.014