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Mat. Zametki, 2006, Volume 80, Issue 4, Pages 536–545 (Mi mz2846)  

This article is cited in 1 scientific paper (total in 1 paper)

When is an Abelian group isomorphic to its endomorphism group?

E. M. Kolenova, A. M. Sebel'din

Nizhny Novgorod State Pedagogical University

Abstract: In the paper, necessary and sufficient conditions for an Abelian group $A$ to be isomorphic to the endomorphism group $\operatorname{End}(A)$ are obtained. The classes of periodic Abelian groups, divisible Abelian groups, nonreduced Abelian groups, and reduced algebraically compact Abelian groups are considered. For certain classes of Abelian groups, the isomorphism problem for a group and its endomorphism group is solved under the assumption that the endomorphism group itself has the corresponding property.

DOI: https://doi.org/10.4213/mzm2846

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English version:
Mathematical Notes, 2006, 80:4, 509–517

Bibliographic databases:

UDC: 512.541
Received: 08.10.2004
Revised: 23.03.2006

Citation: E. M. Kolenova, A. M. Sebel'din, “When is an Abelian group isomorphic to its endomorphism group?”, Mat. Zametki, 80:4 (2006), 536–545; Math. Notes, 80:4 (2006), 509–517

Citation in format AMSBIB
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\pages 536--545
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    This publication is cited in the following articles:
    1. E. M. Kolenova, T. A. Pushkova, “Abelian RE-Groups”, Math. Notes, 107:4 (2020), 595–599  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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