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Mat. Sb., 2013, Volume 204, Number 12, Pages 119–126 (Mi msb8216)  

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

Systems of elements preserving measure on varieties of groups

E. I. Timoshenko

Novosibirsk State Technical University

Abstract: It is proved that for any $l$, $1\leq l\leq r$, a system of elements $ \{v_1,…,v_l\}$ of a free metabelian group $S$ of rank $r\geq2$ is primitive if and only if it preserves measure on the variety of metabelian groups $\mathfrak A^2$. From this we obtain the result that a system of elements $\{v_1,…,v_l\}$ is primitive in the group $S$ if and only if it is primitive in its profinite completion $\widehat{S}$. Furthermore, it is proved that there exist a variety $\mathfrak M$ and a nonprimitive element $v \in F_r(\mathfrak M)$ such that $v$ preserves measure on $\mathfrak M$.
Bibliography: 13 titles.

Keywords: variety of groups, metabelian group, soluble group, primitive system of elements, measure-preserving system of elements.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00084
Ministry of Education and Science of the Russian Federation 14.В37.21.0359


DOI: https://doi.org/10.4213/sm8216

Full text: PDF file (465 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:12, 1811–1818

Bibliographic databases:

Document Type: Article
UDC: 512.54
MSC: Primary 20E10; Secondary 20E18
Received: 29.01.2013 and 21.06.2013

Citation: E. I. Timoshenko, “Systems of elements preserving measure on varieties of groups”, Mat. Sb., 204:12 (2013), 119–126; Sb. Math., 204:12 (2013), 1811–1818

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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, “Distribution of elements on nilpotent groups”, Dokl. Math., 90:1 (2014), 507–508  crossref  crossref  zmath  isi  elib  elib  scopus
    2. 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
    3. E. N. Poroshenko, E. I. Timoshenko, “Uniformly distributed systems of elements on metabelian Lie rings”, Comm. Algebra, 44:4 (2016), 1531–1547  crossref  mathscinet  zmath  isi  scopus
    4. V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev, “Primitivnye i pochti primitivnye elementy svobodnykh algebr shraierovykh mnogoobrazii”, Fundament. i prikl. matem., 21:2 (2016), 3–35  mathnet  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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