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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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