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December 2021 Third homology of perfect central extensions
B. Mirzaii, F. Y. Mokari, D. C. Ordinola
Adv. Studies: Euro-Tbilisi Math. J. 14(4): 61-80 (December 2021). DOI: 10.3251/asetmj/1932200814

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 $H_3(G,\mathbb{Z}) \to H_3(Q, \mathbb{Z})$.

Citation

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B. Mirzaii. F. Y. Mokari. D. C. Ordinola. "Third homology of perfect central extensions." Adv. Studies: Euro-Tbilisi Math. J. 14 (4) 61 - 80, December 2021. https://doi.org/10.3251/asetmj/1932200814

Information

Received: 4 June 2021; Accepted: 3 September 2021; Published: December 2021
First available in Project Euclid: 16 December 2021

Digital Object Identifier: 10.3251/asetmj/1932200814

Subjects:
Primary: 20J06
Secondary: 19D55 , 55P20

Keywords: homology of groups , perfect central extensions , Serre fibrations

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 4 • December 2021
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