##  [Exponent](/exponent) 

  ##  [Exponent](https://puremath.quantumdictionary.io/exponent-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a finite group, the exponent is the least common multiple of the orders of all elements; more generally it is the smallest positive integer n such that g^n = e for every element g when such an integer exists, otherwise the group is said to have infinite exponent.

 

 

 

 

 





 

 



 ##  [Exponent](https://algebra.quantumdictionary.io/exponent-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The exponent of an algebraic structure (commonly a group) is the least common multiple of the orders of all its elements, equivalently the smallest positive integer m such that x^m equals the neutral element for every element x; if no such m exists the exponent is said to be infinite.