A limit approach to group homology

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dc.creatorEmmanouil, Ioannis
dc.creatorMikhailov, Roman
dc.date2008-12-11
dc.date.accessioned2026-07-07T12:11:57Z
dc.date.available2026-07-07T12:11:57Z
dc.descriptionIn this paper, we consider for any free presentation $G = F/R$ of a group $G$ the coinvariance $H_{0}(G,R_{ab}^{\otimes n})$ of the $n$-th tensor power of the relation module $R_{ab}$ and show that the homology group $H_{2n}(G,{\mathbb Z})$ may be identified with the limit of the groups $H_{0}(G,R_{ab}^{\otimes n})$, where the limit is taken over the category of these presentations of $G$. We also consider the free Lie ring generated by the relation module $R_{ab}$, in order to relate the limit of the groups $γ_{n}R/[γ_{n}R,F]$ to the $n$-torsion subgroup of $H_{2n}(G,{\mathbb Z})$.
dc.identifierhttps://arxiv.org/abs/0812.2092
dc.identifierhttp://arxiv.org/abs/0812.2092
dc.identifierJournal of Algebra, 319, (2008), 1450-1461
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210391
dc.subjectGroup Theory
dc.subjectK-Theory and Homology
dc.titleA limit approach to group homology
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