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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
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
Citation:
O. V. Mel'nikov, “Subgroups and homology of free products of profinite groups”, Math. USSR-Izv., 34:1 (1990), 97–119
Linking options:
https://www.mathnet.ru/eng/im1163https://doi.org/10.1070/IM1990v034n01ABEH000607 https://www.mathnet.ru/eng/im/v53/i1/p97
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Abstract page: | 367 | Russian version PDF: | 135 | English version PDF: | 20 | References: | 48 | First page: | 1 |
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