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Matematicheskie Zametki, 2015, Volume 97, Issue 6, Pages 936–941
DOI: https://doi.org/10.4213/mzm10471 (Mi mzm10471) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups

S. A. Shakhova

Altai State University, Barnaul
Full-text PDF (440 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10471
Abstract: It is proved that divisible groups and only these groups are absolutely closed (with respect to the operator of dominion) in the class of $2$-step nilpotent torsion-free groups. It is established that the additive group of the rationals is $1$-closed in an arbitrary quasivariety of nilpotent torsion-free groups and $3$-closed in an arbitrary quasivariety of $2$-step nilpotent torsion-free groups.
Keywords: quasivariety, divisible group, torsion-free group, dominion, absolutely closed group, $2$-step nilpotent torsion-free group.
Received: 03.02.2014
Revised: 08.07.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 6, Pages 946–950
DOI: https://doi.org/10.1134/S0001434615050302
Bibliographic databases:
Document Type: Article
UDC: 512.54.01
Language: Russian
Citation: S. A. Shakhova, “Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups”, Mat. Zametki, 97:6 (2015), 936–941; Math. Notes, 97:6 (2015), 946–950
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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