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

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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.

Relation with other properties

Stronger properties

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