Group of finite exponent

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Group of finite exponent, all facts related to Group of finite exponent) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite group				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
periodic group	all elements have finite order, but there need not be a uniform bound on the orders of elements.				|FULL LIST, MORE INFO