Group of finite exponent

Definition
A group of finite exponent is a group satisfying the following equivalent conditions:


 * 1) Its exponent is a finite natural number. In other words, all the elements of the group have finite order, and the lcm of the orders of all elements (which is how the exponent is defined) is finite.
 * 2) The maximum of element orders is a finite natural number. In other words, all the elements of the group have finite order, and the maximum of the orders of all elements is finite.

Weaker properties
{| class="sortable" border="1" ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
 * Stronger than::periodic group || all elements have finite order, but there need not be a uniform bound on the orders of elements. || || || ||
 * Stronger than::periodic group || all elements have finite order, but there need not be a uniform bound on the orders of elements. || || || ||