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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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\pages 199--207
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http://mi.mathnet.ru/eng/smj2413 http://mi.mathnet.ru/eng/smj/v54/i1/p199
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:
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E. I. Timoshenko, “Systems of elements preserving measure on varieties of groups”, Sb. Math., 204:12 (2013), 1811–1818
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E. I. Timoshenko, “Distribution of elements on nilpotent groups”, Dokl. Math., 90:1 (2014), 507–508
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E. I. Timoshenko, “Distributions of elements on nilpotent varieties of groups”, Sb. Math., 206:3 (2015), 470–479
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E. N. Poroshenko, E. I. Timoshenko, “Uniformly distributed systems of elements on metabelian Lie rings”, Commun. Algebr., 44:4 (2016), 1531–1547
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