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Title: On the torsion of group extensions and group actions
Keywords: Group extension
Group action
Free group action
Torsion group
(Co)-homology of groups
Homotopy equivalence
Issue Date: 2004
Publisher: elsevier
Citation: Bulletin des Sciences Mathématiques, Volume 128, Issue 10, November 2004, Pages 829–837
Abstract: In this note, we study the torsion of extensions of finitely generated abelian by elementary abelian groups. When the action is trivial View the MathML source, we make a specific choice of a 1-cochain for a vanishing multiple of the cohomology class defining the extension and use it to completely describe the torsion of central extensions. As an application, one gets that, under the assumption of trivial action on homology, Zpr may act freely on (S1)k if and only if r⩽k, providing an alternative proof of the main theorem in [Trans. Amer. Math. Soc. 352 (6) (2000) 2689–2700] for central extensions.
ISSN: 0007-4497
Appears in Collections:Δημοσιεύσεις σε Περιοδικά

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