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Near Isomorphism for Countable-Rank Torsion-Free Abelian Groups

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Abstract

The notion of a near isomorphism is extended from finite-rank torsion-free Abelian groups to some classes of infinite-rank groups. The equivalence of different formulations of this notion for a certain class of countable-rank groups is proved.

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References

  1. D. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., Vol. 931, Springer, Berlin (1982).

  2. E. Blagoveshchenskaya, “Direct decompositions of local almost completely decomposable groups of countable rank,” Chebyshevskii Sb., 6, No. 4. 26–49 (2005).

  3. E. Blagoveshchenskaya, Almost Completely Decomposable Abelian Groups and Their Endomorphism Rings [in Russian], Math. Polytech. Univ., St. Petersburg (2009).

  4. E. Blagoveshchenskaya and R. Göbel, “Classification and direct decompositions of some Butler groups of countable rank,” Commun. Algebra, 30, No. 7, 3403–3427 (2002).

    Article  MathSciNet  Google Scholar 

  5. E. Blagoveshchenskaya, R. Göbel, and L. Strüngmann, “Classification of some Butler groups of infinite rank,” Commun. Algebra, 380, 1–17 (2013).

    Article  MathSciNet  Google Scholar 

  6. E. Blagoveshchenskaya and D. Kunetz, “Direct decomposition theory of torsion-free Abelian groups of finite rank: graph method,” Lobachevskii J. Math., 39, No. 1, 29–34 (2018).

    Article  MathSciNet  Google Scholar 

  7. E. Blagoveshchenskaya and L. Strüngmann, “Near-isomorphism for a class of infinite rank torsion-free Abelian groups,” Commun. Algebra, 35, 1–18 (2007).

    Article  MathSciNet  Google Scholar 

  8. E. Blagoveshchenskaya and L. H. Strüngmann, “Direct decomposition theory under near-isomorphism for a class of infinite rank torsion-free Abelian groups,” J. Group Theory, 20, No. 2, 325–346 (2017).

    Article  MathSciNet  Google Scholar 

  9. R. G. Burkovsky, Yu. Bronwald, D. Andronikova, B. Wehinger, M. Krisch, J. Jacobs, D. Gambetti, K. Roleder, A. Majchrowski, A. V. Filimonov, A. I. Rudskoy, S. B. Vakhrushev, and A. K. Tagantsev, “Critical scattering and incommensurate phase transition in antiferroelectric Pb ZrO3 under pressure,” Sci. Reports, 7, 41512 (2017).

    Google Scholar 

  10. L. Fuchs, Infinite Abelian Groups, Vols. 1, 2, Academic Press, London (1970, 1973).

  11. A. Mader, Almost Completely Decomposable Abelian Groups, Algebra, Logic Appl., Vol. 13, Gordon and Breach, Amsterdam (1999).

  12. A. A. Naberezhnov, N. Porechnaya, V. Nizhankovskii, A. Filimonov, and B. Nacke, “Morphology and magnetic properties of ferriferous two-phase sodium borosilicate glasses,” Sci. World J., 2014, 320451 (2014).

    Article  Google Scholar 

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Authors and Affiliations

  1. Emperor Alexander I St. Petersburg State Transport University, Moskovsky prospect 9, St. Petersburg, 190031, Russia

    E. A. Blagoveshchenskaya

  2. Peter the Great St. Petersburg Polytechnic University, Politekhnicheskaya 29, St. Petersburg, 195251, Russia

    E. A. Blagoveshchenskaya & A. V. Filimonov

  3. Branch of the joint-stock company “Radio Engineering Concern Vega” in St. Petersburg, 14a Akademika Pavlova str., St. Petersburg, 197376, Russia

    A. E. Trifonov

Authors
  1. E. A. Blagoveshchenskaya
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  2. A. V. Filimonov
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  3. A. E. Trifonov
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Corresponding author

Correspondence to E. A. Blagoveshchenskaya.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 17–28, 2019.

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Blagoveshchenskaya, E.A., Filimonov, A.V. & Trifonov, A.E. Near Isomorphism for Countable-Rank Torsion-Free Abelian Groups. J Math Sci 259, 394–402 (2021). https://doi.org/10.1007/s10958-021-05628-4

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  • DOI: https://doi.org/10.1007/s10958-021-05628-4

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