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Mathematics of the USSR-Izvestiya, 1990, Volume 34, Issue 1, Pages 97–119
DOI: https://doi.org/10.1070/IM1990v034n01ABEH000607
(Mi im1163)
 

This article is cited in 31 scientific papers (total in 31 papers)

Subgroups and homology of free products of profinite groups

O. V. Mel'nikov
References:
Abstract: The author defines a new construction of free product $G=\mathop{\text{\LARGE{$*$}}}^{\mathfrak K}_TG_t$ in the variety $\mathfrak K$ of profinite groups of the family $\{G_t\mid t\in T\}$ of groups in $\mathfrak K$, continuously indexed by points of the profinite space $T$. In the case where $\mathfrak K$ is closed relative to extensions with Abelian kernels, a number of assertions about the homology groups of $G$ are obtained. Using homological methods, a theorem of Kurosh type on decomposition of an arbitrary pro-$p$-subgroup in $G$ into a free pro-$p$-product is proved, under a certain separability condition on $G$.
Bibliography: 19 titles.
Received: 06.05.1987
Bibliographic databases:
UDC: 512.546.37
MSC: Primary 20E06, 20E18, 20E07; Secondary 20J05
Language: English
Original paper language: Russian
Citation: O. V. Mel'nikov, “Subgroups and homology of free products of profinite groups”, Math. USSR-Izv., 34:1 (1990), 97–119
Citation in format AMSBIB
\Bibitem{Mel89}
\by O.~V.~Mel'nikov
\paper Subgroups and homology of free products of profinite groups
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 97--119
\mathnet{http://mi.mathnet.ru//eng/im1163}
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000607}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=992980}
\zmath{https://zbmath.org/?q=an:0684.20019|0671.20025}
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  • https://doi.org/10.1070/IM1990v034n01ABEH000607
  • https://www.mathnet.ru/eng/im/v53/i1/p97
  • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:367
    Russian version PDF:135
    English version PDF:20
    References:48
    First page:1
     
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