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Algebra Logika, 2006, Volume 45, Number 4, Pages 447–457 (Mi al154)  

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

Computing Test Rank for a Free Solvable Group

E. I. Timoshenko

Novosibirsk State University of Architecture and Civil Engineering

Abstract: It is proved that test rank of a free solvable non-Abelian group of finite rank is 1 less than the rank of that group. This gives the answer to Question 14.88 posed in the Kourovka Notebook by Fine and Shpilrain, asking whether or not a free solvable group of rank 2 and solvability index $n\geqslant3$ has test elements.

Keywords: free solvable group, test element

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English version:
Algebra and Logic, 2006, 45:4, 254–260

Bibliographic databases:

UDC: 512.5
Received: 20.01.2006

Citation: E. I. Timoshenko, “Computing Test Rank for a Free Solvable Group”, Algebra Logika, 45:4 (2006), 447–457; Algebra and Logic, 45:4 (2006), 254–260

Citation in format AMSBIB
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\by E.~I.~Timoshenko
\paper Computing Test Rank for a Free Solvable Group
\jour Algebra Logika
\yr 2006
\vol 45
\issue 4
\pages 447--457
\mathnet{http://mi.mathnet.ru/al154}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287650}
\zmath{https://zbmath.org/?q=an:1115.20030}
\elib{https://elibrary.ru/item.asp?id=9234328}
\transl
\jour Algebra and Logic
\yr 2006
\vol 45
\issue 4
\pages 254--260
\crossref{https://doi.org/10.1007/s10469-006-0023-6}
\elib{https://elibrary.ru/item.asp?id=13514009}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748944343}


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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. Ch. K. Gupta, E. I. Timoshenko, “The test rank of a soluble product of free Abelian groups”, Sb. Math., 199:4 (2008), 495–510  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. E. I. Timoshenko, M. A. Shevelin, “Computing the test rank of a free solvable Lie algebra”, Siberian Math. J., 49:6 (2008), 1131–1135  mathnet  crossref  mathscinet  isi
    3. Oguslu N.S., Ekici N., “the Test Rank of a Solvable Product of Free Abelian Lie Algebras”, J. Algebra. Appl., 18:2 (2019), 1950025  crossref  mathscinet  zmath  isi  scopus
    4. V. A. Roman'kov, E. I. Timoshenko, “Verbally closed subgroups of free solvable groups”, Algebra and Logic, 59:3 (2020), 253–265  mathnet  crossref  crossref  isi
    5. E. I. Timoshenko, “Retrakty i verbalno zamknutye podgruppy otnositelno svobodnykh razreshimykh grupp”, Sib. matem. zhurn., 62:3 (2021), 659–667  mathnet  crossref  elib
  • Алгебра и логика Algebra and Logic
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