##  [Moufang Identity](/moufang-identity) 

  ##  [Moufang Identity](https://puremath.quantumdictionary.io/moufang-identity-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algebraic identity satisfied in certain loops (nonassociative group-like structures), typically written in forms such as (ab)(ca)=a(bc)a for all elements a,b,c; when a loop satisfies any one of the equivalent Moufang identities it is called a Moufang loop, which recovers many group-like associativity consequences without full associativity.