First-order axiomatization of torsion-free groups
= First-order axiomatization of torsion-free groups
The torsion-free groups are axiomatized by the group axioms together with, for every integer $n\geq2$,
$$
\forall x\,(x^n=e\Rightarrow x=e).
$$
= First-order axiomatization of torsion-free groups
The torsion-free groups are axiomatized by the group axioms together with, for every integer $n\geq2$,
$$
\forall x\,(x^n=e\Rightarrow x=e).
$$