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Algebra Logika, 2003, Volume 42, Number 1, Pages 37–50 (Mi al16)  

This article is cited in 7 scientific papers (total in 7 papers)

Test Rank for Some Free Polynilpotent Groups

Ch. K. Guptaa, E. I. Timoshenko

a University of Manitoba

Abstract: We prove a theorem on possible test rank values for groups of the form $F/R'$. It is shown that test rank of a free polynilpotent group $F_r(\mathbb{A}\mathbb{N}_{c_1}\ldots\mathbb{N}_{c_l})$ is equal to $r-1$ or $r$, for any $r \geqslant 2$ and every collection $(c_1,\ldots,c_l)$ of classes. Moreover, $tr(F_r(\mathbb{A}\mathbb{N}_c))=r-1$ for $r\geqslant 2$ and $c\geqslant 2$.

Keywords: test rank, polynilpotent group, free group.

Full text: PDF file (194 kB)
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English version:
Algebra and Logic, 2003, 42:1, 20–28

Bibliographic databases:

UDC: 512.5
Received: 25.02.2001

Citation: Ch. K. Gupta, E. I. Timoshenko, “Test Rank for Some Free Polynilpotent Groups”, Algebra Logika, 42:1 (2003), 37–50; Algebra and Logic, 42:1 (2003), 20–28

Citation in format AMSBIB
\Bibitem{GupTim03}
\by Ch.~K.~Gupta, E.~I.~Timoshenko
\paper Test Rank for Some Free Polynilpotent Groups
\jour Algebra Logika
\yr 2003
\vol 42
\issue 1
\pages 37--50
\mathnet{http://mi.mathnet.ru/al16}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988022}
\zmath{https://zbmath.org/?q=an:1034.20032}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 1
\pages 20--28
\crossref{https://doi.org/10.1023/A:1022624723429}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746457766}


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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, “Criterion for Invertibility of Endomorphisms and Test Rank of Metabelian Products of Abelian Groups”, Algebra and Logic, 43:5 (2004), 316–326  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Ch. K. Gupta, E. I. Timoshenko, “First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups”, Siberian Math. J., 47:4 (2006), 634–642  mathnet  crossref  mathscinet  zmath  isi
    3. E. I. Timoshenko, “Computing Test Rank for a Free Solvable Group”, Algebra and Logic, 45:4 (2006), 254–260  mathnet  crossref  mathscinet  zmath  elib  elib
    4. Esmerligil Z., Kahyalar D., Ekici N., “Test rank of F/R ' Lie algebras”, International Journal of Algebra and Computation, 16:4 (2006), 817–825  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. 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
    7. Ekici N., Oguslu N.S., “Test rank of an abelian product of a free Lie algebra and a free abelian Lie algebra”, Proc Indian Acad Sci Math Sci, 121:3 (2011), 291–300  crossref  mathscinet  zmath  isi  elib  scopus
  • Алгебра и логика Algebra and Logic
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