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

Bibliographic databases:

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

Citation in format AMSBIB
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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, “Primitive and almost primitive elements of Schreier varieties”, J. Math. Sci., 237:2 (2019), 157–179  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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