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Algebra Logika, 2015, Volume 54, Number 4, Pages 503–519 (Mi al707)  

This article is cited in 2 scientific papers (total in 2 papers)

Endomorphisms of free solvable groups preserving primitivity of systems of elements

E. I. Timoshenko

Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630092, Russia

Abstract: It is proved that an endomorphism of a free metabelian group $S_r$ of any finite rank $r$ that preserves primitivity of systems of elements is an automorphism; in addition, every primitive endomorphism of a free solvable group of rank 2 is an automorphism.

Keywords: free metabelian group, free solvable group, endomorphism, automorphism.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-01485
Ministry of Education and Science of the Russian Federation 2014/138, проект 1052
Supported by RFBR (project No. 15-01-01485) and by the Russian Ministry of Education and Science (gov. contract 2014/138, project No. 1052).


DOI: https://doi.org/10.17377/alglog.2015.54.406

Full text: PDF file (190 kB)
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English version:
Algebra and Logic, 2015, 54:4, 323–335

Bibliographic databases:

UDC: 512.5
Received: 06.05.2014
Revised: 16.11.2014

Citation: E. I. Timoshenko, “Endomorphisms of free solvable groups preserving primitivity of systems of elements”, Algebra Logika, 54:4 (2015), 503–519; Algebra and Logic, 54:4 (2015), 323–335

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev, “Primitive and almost primitive elements of Schreier varieties”, J. Math. Sci., 237:2 (2019), 157–179  mathnet  crossref  elib
    2. E. I. Timoshenko, “O primitivnykh i vnutrennikh endomorfizmakh grupp”, Sib. matem. zhurn., 61:2 (2020), 418–427  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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