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Vanishing ranges for the mod p cohomology of alternating subgroups of Coxeter groups

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Title: Vanishing ranges for the mod p cohomology of alternating subgroups of Coxeter groups
Authors: Akita, Toshiyuki Browse this author
Liu, Ye Browse this author
Keywords: Group cohomology
Coxeter groups
Alternating subgroups
Issue Date: 1-Mar-2017
Publisher: Elsevier
Journal Title: Journal of Algebra
Volume: 473
Start Page: 132
End Page: 141
Publisher DOI: 10.1016/j.jalgebra.2016.11.005
Abstract: We obtain vanishing ranges for the mod p cohomology of alternating subgroups of finite p-free Coxeter groups. Here a Coxeter group W is p-free if the order of the product st is prime to p for every pair of Coxeter generators s, t of W. Our result generalizes those for alternating groups formerly proved by Kleshchev-Nakano and Burichenko. As a byproduct, we obtain vanishing ranges for the twisted cohomology of finite p-free Coxeter groups with coefficients in the sign representations. In addition, a weak version of the main result is proved for a certain class of infinite Coxeter groups. (C) 2016 Elsevier Inc. All rights reserved.
Rights: ©2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
http://creativecommons.org/licenses/by-nc-nd/4.0/
Type: article
URI: http://hdl.handle.net/2115/72709
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 秋田 利之

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