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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 10, Pages 60–73 (Mi ivm8745)  

This article is cited in 8 scientific papers (total in 8 papers)

Abelian groups with nilpotent commutators of endomorphisms

A. R. Chekhlov

Chair of Algebra, Tomsk State University, Tomsk, Russia

Abstract: We study classes of abelian groups with nilpotent commutators of their endomorphisms, as well as groups with a semirigid condition imposed on direct summands. We describe these groups amongst separable, vector, and algebraically compact torsion-free groups. We construct examples illustrating the distinction between considered classes of groups, as well as $E$-solvable and $E$-nilpotent groups.

Keywords: commutatorically invariant subgroup, $E$-nilpotent and $E$-solvable groups, $E$-engelian group, power $E$-commutant.

Full text: PDF file (286 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:10, 50–61

Bibliographic databases:

UDC: 512.541
Received: 09.09.2011

Citation: A. R. Chekhlov, “Abelian groups with nilpotent commutators of endomorphisms”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 10, 60–73; Russian Math. (Iz. VUZ), 56:10 (2012), 50–61

Citation in format AMSBIB
\Bibitem{Che12}
\by A.~R.~Chekhlov
\paper Abelian groups with nilpotent commutators of endomorphisms
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 10
\pages 60--73
\mathnet{http://mi.mathnet.ru/ivm8745}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137059}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 10
\pages 50--61
\crossref{https://doi.org/10.3103/S1066369X12100052}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84869481234}


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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. A. R. Chekhlov, “Torsion-Free Weakly Transitive $E$-Engel Abelian Groups”, Math. Notes, 94:4 (2013), 583–589  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. R. Chekhlov, “O pryamykh summakh tsiklicheskikh grupp s invariantnymi monomorfizmami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 3(23), 60–65  mathnet  elib
    3. A. R. Chekhlov, Ml. V. Agafontseva, “Ob abelevykh gruppakh s tsentralnymi kvadratami kommutatorov endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 4(24), 54–59  mathnet  elib
    4. A. R. Chekhlov, “On abelian groups with commuting monomorphisms”, Siberian Math. J., 54:5 (2013), 946–950  mathnet  crossref  mathscinet  isi
    5. A. R. Chekhlov, “On abelian groups with right-invariant isometries”, Siberian Math. J., 55:3 (2014), 574–577  mathnet  crossref  mathscinet  isi  elib  elib
    6. Chekhlov A.R., Danchev P.V., “on Commutator Fully Transitive Abelian Groups”, J. Group Theory, 18:4 (2015), 623–647  crossref  mathscinet  zmath  isi  elib
    7. A. R. Chekhlov, “On Abelian groups with commutative commutators of endomorphisms”, J. Math. Sci., 230:3 (2018), 502–506  mathnet  crossref  mathscinet  elib
    8. A. R. Chekhlov, “Vpolne inertnye podgruppy vpolne razlozhimykh grupp konechnogo ranga i ikh soizmerimost”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 3(41), 42–50  mathnet  crossref  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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