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Model. Anal. Inform. Sist., 2013, Volume 20, Number 1, Pages 133–137 (Mi mais291)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Root-Class Residuallity of Generalized Free Products

E. A. Tumanova

Ivanovo State University, Ivanovo, Russia

Abstract: Let $\mathcal{K}$ be a root class of groups. It is proved that a free product of any family of residually $\mathcal{K}$ groups with one amalgamated subgroup, which is a retract in all free factors, is residually $\mathcal{K}$. The sufficient condition for a generalized free product of two groups to be residually $\mathcal{K}$ is also obtained, provided that the amalgamated subgroup is normal in one of the free factors and is a retract in another.

Keywords: free product with one amalgamated subgroup, root class of groups, root-class residuallity, retract.

Full text: PDF file (284 kB)
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UDC: 512.543
Received: 22.12.2012

Citation: E. A. Tumanova, “On the Root-Class Residuallity of Generalized Free Products”, Model. Anal. Inform. Sist., 20:1 (2013), 133–137

Citation in format AMSBIB
\Bibitem{Tum13}
\by E.~A.~Tumanova
\paper On the Root-Class Residuallity of Generalized Free Products
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 1
\pages 133--137
\mathnet{http://mi.mathnet.ru/mais291}


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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. D. I. Moldavanskii, “Kombinatornaya teoriya grupp v Ivanovskom gosudarstvennom universitete”, Chebyshevskii sb., 15:4 (2014), 32–54  mathnet
    2. E. A. Tumanova, “On the root-class residuality of generalized free products with a normal amalgamation”, Russian Math. (Iz. VUZ), 59:10 (2015), 23–37  mathnet  crossref
    3. E. V. Sokolov, E. A. Tumanova, “Sufficient conditions for the root-class residuality of certain generalized free products”, Siberian Math. J., 57:1 (2016), 135–144  mathnet  crossref  crossref  mathscinet  isi  elib
    4. E. V. Sokolov, E. A. Tumanova, “Root Class Residuality of HNN-Extensions with Central Cyclic Associated Subgroups”, Math. Notes, 102:4 (2017), 556–568  mathnet  crossref  crossref  mathscinet  isi  elib
    5. E. A. Tumanova, “The root class residuality of the tree product of groups with amalgamated retracts”, Siberian Math. J., 60:4 (2019), 699–708  mathnet  crossref  crossref  isi  elib
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