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This article is cited in 16 scientific papers (total in 16 papers)
Subgroups and homology of free products of profinite groups
O. V. Mel'nikov
Abstract:
The author defines a new construction of free product
$G=\mathop{ŁARGE{$*$}}^{\mathfrak K}_TG_t$ 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.
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:1, 97–119
Bibliographic databases:
 
UDC:
512.546.37
MSC: Primary 20E06, 20E18, 20E07; Secondary 20J05
Received: 06.05.1987
Citation:
O. V. Mel'nikov, “Subgroups and homology of free products of profinite groups”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989), 97–120; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 1
\pages 97--120
\mathnet{http://mi.mathnet.ru/izv1163}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=992980}
\zmath{https://zbmath.org/?q=an:0684.20019|0671.20025}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 97--119
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000607}
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