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

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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## 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 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 $m$.

## Facts

The general linear group over the integers has this property. For full proof, refer: Order of periodic element of general linear group over integers is bounded