Torsion group
= Torsion group
A <group> is a torsion group when every element is a <torsion element>, meaning that each element has finite order. The orders need not have a common finite bound. A torsion group has no nontrivial <torsion-free group> as a subgroup; in particular it cannot contain a nonabelian <free group>. Infinite <finitely generated groups> of this kind can be constructed using a <torsion group construction by p-power relators>.