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- W2040259521 abstract "In this note, we study the torsion of extensions of finitely generated abelian by elementary abelian groups. When the action is trivial (modp), 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. Dans cette Note, nous étudions la torsion des extensions des groupes abéliens de type fini par des groupes abéliens élémentaires. Lorsque l'action est triviale (modp), nous effectuons un choix particulier de 1-cochaı̂ne pour un multiple de la classe de cohomologie définissant l'extension, dont nous nous servons afin de décrire complètement la torsion des extensions centrales. En application, il en découle que sous l'hypothèse supplémentaire d'action triviale en homologie, Zrp ne peut agir sur (S1)k que si et seulement si r⩽k, ce qui fournit par ailleurs, une preuve entièrement différente du théorème principal dans [Trans. Amer. Math. Soc. 352 (6) (2000) 2689–2700] pour des extensions centrales." @default.
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- W2040259521 date "2004-11-01" @default.
- W2040259521 modified "2023-09-27" @default.
- W2040259521 title "On the torsion of group extensions and group actions" @default.
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- W2040259521 doi "https://doi.org/10.1016/j.bulsci.2004.04.004" @default.
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