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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 1, Pages 97–120 (Mi izv1163)  

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. A. Zalesskii, “The structure of the congruence kernel for $\mathrm{SL}_2$ in the case of a global field of positive characteristic”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 489–495  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. P. A. Zalesskii, “Normal subgroups of free constructions of profinite groups and the congruence kernel in the case of positive characteristic”, Izv. Math., 59:3 (1995), 499–516  mathnet  crossref  mathscinet  zmath  isi
    3. V. M. Tsvetkov, “On some 2-extension of the field $\mathbb Q$ of rational numbers”, J. Math. Sci. (New York), 95:2 (1999), 2161–2163  mathnet  crossref  mathscinet  zmath
    4. Ido Efrat, “Pro-pGalois Groups of Algebraic Extensions of”, Journal of Number Theory, 64:1 (1997), 84  crossref
    5. Herfort W., Zalesskii P., “Cyclic Extensions of Free Pro-P Groups”, J. Algebra, 216:2 (1999), 511–547  crossref  mathscinet  zmath  isi
    6. Yu.L.. Ershov, “ON FREE PRODUCTS OF ABSOLUTE GALOIS GROUPS. II”, Communications in Algebra, 29:9 (2001), 3773  crossref
    7. O. V. Mel'nikov, “Aspherical pro-$p$-groups”, Sb. Math., 193:11 (2002), 1639–1670  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. W Herfort, P. A Zalesskii, “Profinite HNN-constructions”, jgth, 10:6 (2007), 799  crossref  mathscinet  zmath  isi
    9. Peter Symonds, “On cohomology isomorphisms of groups”, Journal of Algebra, 313:2 (2007), 802  crossref
    10. Luis Ribes, “Pro-p groups that act on profinite trees”, jgth, 11:1 (2008), 75  crossref  mathscinet  zmath  isi
    11. Peter Symonds, “Double Coset Formulas for Profinite Groups”, Communications in Algebra, 36:3 (2008), 1059  crossref
    12. D. H. Kochloukova, P. A. Zalesskii, “On pro-p analogues of limit groups via extensions of centralizers”, Math Z, 2009  crossref
    13. Wolfgang Herfort, Pavel A. Zalesskii, “A virtually free pro-p need not be the fundamental group of a profinite graph of finite groups”, Arch Math, 2009  crossref  isi
    14. D.H. Kochloukova, P.A. Zalesskii, “Fully residually free pro-p groups”, Journal of Algebra, 324:4 (2010), 782  crossref
    15. Dessislava Kochloukova, Pavel Zalesskii, “Subgroups and homology of extensions of centralizers of pro-pgroups”, Math. Nachr, 2014, n/a  crossref
    16. D.H.. KOCHLOUKOVA, P.A.. ZALESSKII, “Subdirect products of pro-p groups”, Math. Proc. Camb. Phil. Soc, 2015, 1  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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