Group in which all elements of finite order have a common bound on order

Definition
A group in which all elements of finite order have a common bound on order is a group satisfying the following equivalent conditions:


 * 1) There exists a natural number $$k$$ such that for any defining ingredient::periodic element of the group, i.e., any element whose order is finite, the order is at most equal to $$k$$.
 * 2) There exists a natural number $$m$$ such that for any periodic element of the group, the order of that element divides $$m$$.

Stronger properties

 * Weaker than::Torsion-free group
 * Weaker than::Bounded-exponent group
 * Weaker than::Finite group

Facts
The general linear group over the integers has this property.