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On Abelian Groups Close to E-Solvable Groups

Abstract

E-nilpotent and E-solvable Abelian groups are studied. The properties of such groups are studied, and examples illustrating the differences and connections between the investigated classes of groups are presented. The structure of E-solvable periodical, completely decomposable, coperiodic, split mixed, and other groups is shown.

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Correspondence to A. R. Chekhlov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 183–219, 2011/12.

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Chekhlov, A.R. On Abelian Groups Close to E-Solvable Groups. J Math Sci 197, 708–733 (2014). https://doi.org/10.1007/s10958-014-1755-9

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Keywords

  • Abelian Group
  • Direct Summand
  • Commutative Ring
  • Endomorphism Ring
  • Periodic Group