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Mat. Sb. (N.S.), 1969, Volume 79(121), Number 4(8), Pages 616–620 (Mi msb3602)  

This article is cited in 9 scientific papers (total in 9 papers)

On free products of groups

A. L. Shmel'kin


Abstract: Let $F=\prod^*G_i$ be a free product with a normal subgroup $R$, and let $V(R)$ be a verbal subgroup of $R$. The main result of this paper asserts that when $R$ is contained in the Cartesian subgroup of $F$, $F/V(R)$ is embeddable in the verbal $V$-wreath product of a $\mathfrak B$-free group by $F/R$ (here $\mathfrak B$ is the variety defined by the laws $V$). This embedding reduces, to a great extent, the study $F/V(R)$ to that of $F/R$ and $R/V(R)$. New as well as known results about $F/V(R)$ are obtained as corollaries of the above-mentioned theorem.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1969, 8:4, 593–597

Bibliographic databases:

UDC: 519.41/47
MSC: 20E06, 20E22, 20K27
Received: 25.12.1968

Citation: A. L. Shmel'kin, “On free products of groups”, Mat. Sb. (N.S.), 79(121):4(8) (1969), 616–620; Math. USSR-Sb., 8:4 (1969), 593–597

Citation in format AMSBIB
\Bibitem{Shm69}
\by A.~L.~Shmel'kin
\paper On free products of groups
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 79(121)
\issue 4(8)
\pages 616--620
\mathnet{http://mi.mathnet.ru/msb3602}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=257235}
\zmath{https://zbmath.org/?q=an:0204.34204}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 4
\pages 593--597
\crossref{https://doi.org/10.1070/SM1969v008n04ABEH002045}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. I. Èidel'kind, “Verbal products of Magnus groups”, Math. USSR-Sb., 14:4 (1971), 501–524  mathnet  crossref  mathscinet  zmath
    2. Yu. A. Kolmakov, “Conjugacy separability of some factor groups of a free product”, Math. USSR-Sb., 60:1 (1988), 67–75  mathnet  crossref  mathscinet  zmath
    3. P. V. Ushakov, “IA-Automorphisms of Metabelian Products of Two Abelian Groups”, Math. Notes, 70:3 (2001), 403–412  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. P. V. Ushakov, “$\operatorname{IA}$-Automorphisms of Free Products of Two Abelian Torsion-Free Groups”, Math. Notes, 70:6 (2001), 830–837  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. N. Remeslennikov, N. S. Romanovskii, “Metabelian Products of Groups”, Algebra and Logic, 43:3 (2004), 190–197  mathnet  crossref  mathscinet  zmath  elib  elib
    6. Ch. K. Gupta, E. I. Timoshenko, “Criterion for Invertibility of Endomorphisms and Test Rank of Metabelian Products of Abelian Groups”, Algebra and Logic, 43:5 (2004), 316–326  mathnet  crossref  mathscinet  zmath  elib  elib
    7. Ch. K. Gupta, E. I. Timoshenko, “The test rank of a soluble product of free Abelian groups”, Sb. Math., 199:4 (2008), 495–510  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. E. I. Timoshenko, “Identities of the soluble product of abelian groups”, Siberian Math. J., 52:2 (2011), 372–376  mathnet  crossref  mathscinet  isi
    9. E. I. Timoshenko, “Normal automorphisms of a soluble product of abelian groups”, Siberian Math. J., 56:1 (2015), 191–198  mathnet  crossref  mathscinet  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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