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Algebra Logika, 2011, Volume 50, Number 3, Pages 368–387 (Mi al491)  

A quasivariety lattice of torsion-free soluble groups

A. L. Polushin

Altai State University, Barnaul, Russia

Abstract: Let $L_q(qG)$ be a lattice of quasivarieties contained in a quasivariety generated by a group $G$. It is proved that if $G$ is a torsion-free finitely generated group in $\mathcal{AB}_{p^k}$, where $p$ is a prime, $p\ne2$, and $k\in\mathbf N$, which is a split extension of an Abelian group by a cyclic group, then the lattice $L_q(qG)$ is a finite chain.

Keywords: quasivariety, quasivariety lattice, metabelian group.

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English version:
Algebra and Logic, 2011, 50:3, 257–271

Bibliographic databases:

UDC: 512.54.01
Received: 05.05.2010
Revised: 17.11.2010

Citation: A. L. Polushin, “A quasivariety lattice of torsion-free soluble groups”, Algebra Logika, 50:3 (2011), 368–387; Algebra and Logic, 50:3 (2011), 257–271

Citation in format AMSBIB
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\paper A quasivariety lattice of torsion-free soluble groups
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\pages 368--387
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