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Algebra i Analiz, 2020, Volume 32, Issue 6, Pages 147–163 (Mi aa1734)  
Research Papers

Parametrized symmetric groups and the second homology of a group

S. Sinchuk

Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
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Abstract: The notion of a symmetric group parametrized by elements of a group is introduced. It is shown that this group is an extension of a subgroup of the wreath product $G \wr S_n$ by $\mathrm{H}_2(G, \mathbb{Z})$. Motivation behind this construction is also discussed.
Keywords: extensions of type $\mathfrak{H}_n(G)$, amalgamated products, van Kampen theorem.
Funding agency Grant number
Russian Science Foundation 19-71-30002
During the final stage of this work the author was supported by the Russian Science Foundation grant №19-71-30002.
Received: 05.12.2019
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 6, Pages 1067–1080
DOI: https://doi.org/10.1090/spmj/1685
Document Type: Article
Language: English
Citation: S. Sinchuk, “Parametrized symmetric groups and the second homology of a group”, Algebra i Analiz, 32:6 (2020), 147–163; St. Petersburg Math. J., 32:6 (2021), 1067–1080
Citation in format AMSBIB
\Bibitem{Sin20}
\by S.~Sinchuk
\paper Parametrized symmetric groups and the second homology of a group
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 6
\pages 147--163
\mathnet{http://mi.mathnet.ru/aa1734}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 6
\pages 1067--1080
\crossref{https://doi.org/10.1090/spmj/1685}
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