This article is cited in 6 papers

On ordering the groups with nilpotent commutant

V. V. Bludov^ab, E. S. Lapshina<sup>c

a</sup> Irkutsk State University
^b Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
^c Irkutsk State Pedagogical University

Abstract: We prove that every group with nilpotent commutant, having an abelian normal subgroup such that the factor by this subgroup is nilpotent, is preorderable if and only if the group is $\Gamma$-torsion-free. An example is exhibited of a nonorderable $\Gamma$-torsion-free group with two-step nilpotent radical. This example demonstrates that for the variety of groups with nilpotent commutant the absence of $\Gamma$-torsion in a group is not a sufficient condition for orderability.

Keywords: orderable group, preorderable group.

UDC: 512.54

Received: 05.03.2002

 English version: Siberian Mathematical Journal, 2003, 44:3, 405–410

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