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Fundam. Prikl. Mat., 2009, Volume 15, Issue 1, Pages 81–98 (Mi fpm1199)  

This article is cited in 3 scientific papers (total in 3 papers)

On finitely generated soluble non-Hopfian groups

V. H. Mikaelian


Abstract: There is a continuum of 3-generator soluble non-Hopfian groups that generate pairwise distinct varieties of groups. Each countable (soluble) group is subnormally embeddable into a 3-generator (soluble) non-Hopfian group. As an illustration to a problem of Neumann, we find a continuum of nonmetanilpotent varieties that contain finitely generated non-Hopfian groups and contain noncountably many pairwise nonisomorphic finitely generated groups.

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English version:
Journal of Mathematical Sciences (New York), 2010, 166:6, 743–755

Bibliographic databases:

UDC: 512.54

Citation: V. H. Mikaelian, “On finitely generated soluble non-Hopfian groups”, Fundam. Prikl. Mat., 15:1 (2009), 81–98; J. Math. Sci., 166:6 (2010), 743–755

Citation in format AMSBIB
\Bibitem{Mik09}
\by V.~H.~Mikaelian
\paper On finitely generated soluble non-Hopfian groups
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 1
\pages 81--98
\mathnet{http://mi.mathnet.ru/fpm1199}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2744948}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 166
\issue 6
\pages 743--755
\crossref{https://doi.org/10.1007/s10958-010-9890-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952291930}


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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. E. V. Kaigorodov, “Khopfovy abelevy gruppy”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2012, no. 2(18), 5–12  mathnet
    2. Vahagn H. Mikaelian, “A geometrical interpretation of infinite wreath powers”, Algebra Discrete Math., 18:2 (2014), 250–267  mathnet  mathscinet
    3. A. I. Budkin, “O gruppakh, ne yavlyayuschikhsya konechno opredelennymi v kazhdom kvazimnogoobrazii grupp”, Sib. elektron. matem. izv., 14 (2017), 937–945  mathnet  crossref
  • Фундаментальная и прикладная математика
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