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Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, Number 1(17), Pages 54–60 (Mi vtgu239)  

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

MATHEMATICS

E-engelian abelian groups of step $\le2$

A. R. Chekhlov

Tomsk State University

Abstract: It is proved that periodicity of the automorphism group or weak transitivity of an E-engelian torsion free group of step $\le2$ implies commutativity of its endomorphism ring. Some properties of the engelian ring of step $2$ are established. It is also shown that the endomorphism ring of a weakly transitive torsion free group is semiprime.

Keywords: commutator of endomorphisms, prime radical, nil radical, E-solvable group, weakly transitive torsion free group.

Full text: PDF file (286 kB)
References: PDF file   HTML file
UDC: 512.541+512.552

Accepted: November 3, 2011

Citation: A. R. Chekhlov, “E-engelian abelian groups of step $\le2$”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, no. 1(17), 54–60

Citation in format AMSBIB
\Bibitem{Che12}
\by A.~R.~Chekhlov
\paper E-engelian abelian groups of step~$\le2$
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2012
\issue 1(17)
\pages 54--60
\mathnet{http://mi.mathnet.ru/vtgu239}


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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. D. S. Chistyakov, “Obobschenie svoistva vpolne tranzitivnosti abelevykh grupp bez krucheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2012, no. 2(18), 52–55  mathnet
    2. 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
    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 commutative commutators of endomorphisms”, J. Math. Sci., 230:3 (2018), 502–506  mathnet  crossref  mathscinet  elib
  • Вестник Томского государственного университета. Математика и механика
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