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Sibirsk. Mat. Zh., 2013, Volume 54, Number 1, Pages 199–207 (Mi smj2413)  

This article is cited in 4 scientific papers (total in 4 papers)

Primitive and measure-preserving systems of elements on the varieties of metabelian and metabelian profinite groups

E. I. Timoshenko

Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: Given a free metabelian group $S$ of finite rank $r$, $r\ge2$, we prove that a system of elements $g_1,…,g_n\in S$ for $n=1$ or $n=r$ preserves measure on the variety of all metabelian groups if and only if the system is primitive. Similar results hold for a free profinite group $\hat S$ and the variety of finite metabelian groups for each $n$, $1\le n\le r$. Some corollaries to these theorems are derived.

Keywords: primitive system of elements, measure-preserving system of elements, metabelian group, profinite group.

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English version:
Siberian Mathematical Journal, 2013, 54:1, 152–158

Bibliographic databases:

UDC: 512.5
Received: 14.02.2012

Citation: E. I. Timoshenko, “Primitive and measure-preserving systems of elements on the varieties of metabelian and metabelian profinite groups”, Sibirsk. Mat. Zh., 54:1 (2013), 199–207; Siberian Math. J., 54:1 (2013), 152–158

Citation in format AMSBIB
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\by E.~I.~Timoshenko
\paper Primitive and measure-preserving systems of elements on the varieties of metabelian and metabelian profinite groups
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 1
\pages 199--207
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\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 1
\pages 152--158
\crossref{https://doi.org/10.1134/S0037446613010199}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874575142}


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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. E. I. Timoshenko, “Systems of elements preserving measure on varieties of groups”, Sb. Math., 204:12 (2013), 1811–1818  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. E. I. Timoshenko, “Distribution of elements on nilpotent groups”, Dokl. Math., 90:1 (2014), 507–508  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. E. I. Timoshenko, “Distributions of elements on nilpotent varieties of groups”, Sb. Math., 206:3 (2015), 470–479  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. E. N. Poroshenko, E. I. Timoshenko, “Uniformly distributed systems of elements on metabelian Lie rings”, Commun. Algebr., 44:4 (2016), 1531–1547  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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