On Ordering the Groups with Nilpotent Commutant |
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Authors: | Bludov V V Lapshina E S |
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Institution: | (1) Irkutsk State University, USSR;(2) Institute of Dynamics of Systems and Control Theory, Irkutsk |
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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 -torsion-free. An example is exhibited of a nonorderable -torsion-free group with two-step nilpotent radical. This example demonstrates that for the variety of groups with nilpotent commutant the absence of -torsion in a group is not a sufficient condition for orderability. |
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Keywords: | orderable group preorderable group |
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