First-order axiomatization of torsion-free groups

The torsion-free groups are axiomatized by the group axioms together with, for every integer

n \geq 2

,

\forall x (x^{n} = e \Rightarrow x = e) .

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Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 16G / ii / Solution

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