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Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, Number 2(18), Pages 5–12 (Mi vtgu247)  

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

MATHEMATICS

Hopfian Abelian groups

E. V. Kaigorodov

Tomsk State University

Abstract: This paper presents the general properties of Hopfian Abelian groups, in particular, those related to direct decompositions. The complete description of Hopfian divisible groups is presented; on the basis of this description, the study of hopficity of arbitrary Abelian groups is reduced to the study of hopficity of reduced groups. Direct sums of cyclic groups that are Hopfian groups are characterized.

Keywords: Abelian group, Hopfian group, divisible group, reduced group, cyclic group.

Full text: PDF file (731 kB)
References: PDF file   HTML file
UDC: 512.541
Received: 15.12.2011

Citation: E. V. Kaigorodov, “Hopfian Abelian groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, no. 2(18), 5–12

Citation in format AMSBIB
\Bibitem{Kay12}
\by E.~V.~Kaigorodov
\paper Hopfian Abelian groups
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2012
\issue 2(18)
\pages 5--12
\mathnet{http://mi.mathnet.ru/vtgu247}


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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. E. V. Kaigorodov, “O dvukh klassakh khopfovykh abelevykh grupp”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 2(22), 22–32  mathnet
    2. E. V. Kaigorodov, “Khopfovy vpolne razlozhimye gruppy bez krucheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 4(24), 24–28  mathnet
    3. E. V. Kaigorodov, “Hopfian algebraically compact Abelian groups”, Algebra and Logic, 52:6 (2014), 442–447  mathnet  crossref  mathscinet  isi
    4. E. V. Kaigorodov, S. M. Chedushev, “Kokhopfovy abelevy gruppy”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2015, no. 4(36), 21–33  mathnet  crossref  elib
    5. E. V. Kaigorodov, P. A. Krylov, “On some classes of Hopfian Abelian groups and modules”, J. Math. Sci., 230:3 (2018), 392–397  mathnet  crossref  mathscinet
  • Вестник Томского государственного университета. Математика и механика
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