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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 1, Pages 199–207
(Mi smj2413)
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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 $g_1,\dots,g_n\in S$ 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.
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
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https://www.mathnet.ru/eng/smj2413 https://www.mathnet.ru/eng/smj/v54/i1/p199
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Abstract page: | 250 | Full-text PDF : | 61 | References: | 49 | First page: | 2 |
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