##  [Conjugation](/conjugation) 

  ##  [Conjugation](https://puremath.quantumdictionary.io/conjugation-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

The map sending an element x to g x g^{-1} for a fixed invertible element g in a group, ring, algebra or similar context; describes the action of an element by inner conjugation and yields an inner automorphism when g is fixed.

 

 

 

 

 





 

 



 ##  [Conjugation](https://algebra.quantumdictionary.io/conjugation-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 operation that sends an element x of an algebraic structure (typically a group or a group-like object) to its conjugate g x g^{-1} by another element g, describing the internal symmetry action by inner automorphisms.