Periodic nilpotent group

Definition
A periodic nilpotent group or locally finite nilpotent group is defined in the following equivalent ways:


 * 1) It is both locally finite (every finitely generated subgroup is finite) and nilpotent.
 * 2) It is both periodic (every element has finite order) and nilpotent.
 * 3) It is a nilpotent group and also a group generated by periodic elements: it has a generating set where all the elements have finite orders.
 * 4) Its defining ingredient::abelianization is a defining ingredient::periodic abelian group.
 * 5) It is a nilpotent group and all the quotient groups between successive members of its lower central series are periodic abelian groups.
 * 6) It is a defining ingredient::restricted direct product of defining ingredient::nilpotent p-groups, with a common bound on their defining ingredient::nilpotency class.