On positive and constructive groups

N. G. Khisamiev

2012

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DOI 10.1134/s0037446612050151
Data confidence 70 medium
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Abstract

Considering a group with unique roots (i.e., an R -group), we give a sufficient condition for the existence of a positive (constructive) enumeration with respect to which the isolator of the commutant is computable. Basing on it, we prove the constructivizability of an R -group that admitting a positive enumeration for which the dimension of the commutant is finite. We obtain a necessary and sufficient condition of constructivizability for a torsion-free nilpotent group for which the dimension of the commutant is finite.