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On ordering the groups with nilpotent commutant. (Russian, English) Zbl 1030.06011
Sib. Mat. Zh. 44, No. 3, 513-520 (2003); translation in Sib. Math. J. 44, No. 3, 405-410 (2003).
Summary: 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.

##### MSC:
 06F15 Ordered groups 20F60 Ordered groups (group-theoretic aspects)
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