Abstract
For a central perfect extension of groups $A \rightarrowtail G \twoheadrightarrow Q$, first we study the natural image of $H_3(A,\mathbb{Z})$ in $H_3(G, \mathbb{Z})$. As a particular case, we show that if the extension is universal this image is 2-torsion. Moreover when the plus-construction of the classifying space of $Q$ is an $H$-space, we also study the kernel of the surjective homomorphism $H_3(G,\mathbb{Z}) \to H_3(Q, \mathbb{Z})$.
Version Information
The current pdf replaces the original pdf file, first available on 16 December 2021. The new version corrects the DOI prefix to read 10.32513.
Citation
B. Mirzaii. F. Y. Mokari. D. C. Ordinola. "Third homology of perfect central extensions." Tbilisi Math. J. 14 (4) 61 - 80, December 2021. https://doi.org/10.32513/asetmj/1932200814
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