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The arithmetic hierarchy of torsion-free nilpotent groups. (English. Russian original) Zbl 0976.20027
Algebra Logika 35, No. 3, 308-313 (1996); translation in Algebra Logic 35, No. 3, 172-175 (1996).
Summary: N. Khisamiev proved that all $$\Sigma^0_n$$-presented Abelian torsion-free groups are $$\Delta^0_n$$-presentable. We prove that for the class of nilpotent torsion-free groups, the situation is different: even the quotient group $$F$$ of a $$\Delta^0_n$$-presented nilpotent group of class 2 by its periodic part may fail to have a $$\Delta^0_n$$-presentation.

MSC:
 20F18 Nilpotent groups 20F05 Generators, relations, and presentations of groups 20A15 Applications of logic to group theory
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