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Algebra Logika, 2007, Volume 46, Number 1, Pages 60–74 (Mi al9)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic growth of averaged Dehn functions for nilpotent groups

V. A. Roman'kov

Omsk State University

Abstract: It is proved that in any finite representation of any finitely generated nilpotent group of nilpotency class $l\geqslant1$, the averaged Dehn function $\sigma(n)$ is subasymptotic w.r.t. the function $n^{l+1}$. As a consequence it is stated that in every finite representation of a free nilpotent group of nilpotency class $l$ of finite rank $r\geqslant2$, the Dehn function $\sigma(n)$ is Gromov subasymptotic.

Keywords: nilpotent group, averaged Dehn function.

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English version:
Algebra and Logic, 2007, 46:1, 37–45

Bibliographic databases:

UDC: 512.54
Received: 20.06.2006
Revised: 19.10.2006

Citation: V. A. Roman'kov, “Asymptotic growth of averaged Dehn functions for nilpotent groups”, Algebra Logika, 46:1 (2007), 60–74; Algebra and Logic, 46:1 (2007), 37–45

Citation in format AMSBIB
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\by V.~A.~Roman'kov
\paper Asymptotic growth of averaged Dehn functions for nilpotent groups
\jour Algebra Logika
\yr 2007
\vol 46
\issue 1
\pages 60--74
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\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 1
\pages 37--45
\crossref{https://doi.org/10.1007/s10469-007-0004-4}
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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. Gilman R., Miasnikov A., Osin D., “Exponentially Generic Subsets of Groups”, Illinois J Math, 54:1 (2010), 371–388  mathscinet  zmath  isi  elib
    2. Gilman R.H., Myasnikov A., Roman'kov V., “Random equations in nilpotent groups”, J Algebra, 352:1 (2012), 192–214  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. V. Men'shov, “Random systems of equations in free abelian groups”, Siberian Math. J., 55:3 (2014), 440–450  mathnet  crossref  mathscinet  isi  elib  elib
  • Алгебра и логика Algebra and Logic
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