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On fully inert subgroups of completely decomposable groups

  • Volume 101, Number 2, February, 2017
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Abstract

The completely decomposable torsion-free Abelian groups with finitely many homogeneous components for which every fully inert subgroup is commensurable with a fully invariant subgroup are described.

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References

  1. D. Dikranjan, A. Giordano Bruno, L. Salce, and S. Virili, “Fully inert subgroups of divisible Abelian groups,” J. Group Theory 16 (6), 915–939 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Dikranjan, L. Salce, and P. Zanardo, “Fully inert subgroups of free Abelian groups,” Period. Math. Hungar 69 (1), 69–78 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Goldsmith, L. Salce, and P. Zanardo, “Fully inert subgroups of Abelian p-groups,” J. Algebra 419, 332–349 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  4. U. Dardano and S. Rinauro, “Inertial automorphisms of an Abelian group,” Rend. Sem. Mat. Univ. Padova 127, 213–233 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  5. U. Dardano and S. Rinauro, “On the ring of inertial endomorphisms of an Abelian group,” Ric. Mat. 63, 103–115 (2014). Suppl. 1

    Article  MathSciNet  MATH  Google Scholar 

  6. V. V. Belyaev, “Inert subgroups in infinite simple groups,” Sibirsk. Mat. Zh. 34 (4), 17–23 (1993) [Siberian Math. J. 34 (4), 606–611 (1993), (1994)].

    MathSciNet  MATH  Google Scholar 

  7. V. V. Belyaev, “Locally finite groups with a finite nonseparable subgroup,” Sibirsk. Mat. Zh. 34 (2), 23–41 (1993) [Siberian Math. J. 34 (2), 218–232 (1993), (1994)].

    MathSciNet  Google Scholar 

  8. V. V. Belyaev, M. Kuzucuoğlu, and E. Seçkin, “Totally inert groups,” Rend. Sem. Mat. Univ. Padova 102, 151–156 (1999).

    MathSciNet  MATH  Google Scholar 

  9. M. R. Dixon, M. J. Evans, and A. Tortora, “On totally inert simple groups,” Cent. Eur. J. Math. 8 (1), 22–25 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. R. Chekhlov, “Fully inert subgroups of completely decomposable group of finite rank and their commensurability,” Vestn. Tomsk. Gos. Univ. Mat. Mekh., No. 3 (41), 42–50 (2016).

    Google Scholar 

  11. L. Fuchs, Infinite Abelian Groups, Vol. 2 (Academic Press, New York–London, 1973; Mir, Moscow, 1977).

    Google Scholar 

  12. P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups (Kluwer Academic Publishers, Dordrecht, 2003); Abelian Groups and Their Endomorphism Groups (Faktorial Press, Moscow, 2007).

    Book  MATH  Google Scholar 

  13. P. A. Krylov and E. I. Podberezina, “The group Hom(A,B) as an Artinian E(B)- or E(A)-module,” Fundam. Prikl. Mat. 13 (3), 81–96 (2007) [J. Math. Sci. (N. Y.) 154 (3), 333–343 (2008)].

    MathSciNet  MATH  Google Scholar 

  14. G. Călugăreanu, “Strongly invariant subgroups,” Glasg. Math. J. 57 (2), 431–443 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. R. Chekhlov and P. V. Danchev, “On Abelian groups having all proper fully invariant subgroups isomorphic,” Comm. Algebra 43 (12), 5059–5073 (2015).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to A. R. Chekhlov.

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Original Russian Text © A. R. Chekhlov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 2, pp. 302–312.

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Chekhlov, A.R. On fully inert subgroups of completely decomposable groups. Math Notes 101, 365–373 (2017). https://doi.org/10.1134/S0001434617010394

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  • DOI: https://doi.org/10.1134/S0001434617010394

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