##  [Frobenius Element](/frobenius-element) 

  ##  [Frobenius Element](https://puremath.quantumdictionary.io/frobenius-element-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The conjugacy class in the Galois group attached to an unramified prime, represented by an automorphism whose action on the residue field is the q-power map (x ↦ x^q), and which encodes how that prime permutes primes in extensions.