##  [Galois Correspondence](/galois-correspondence) 

  ##  [Galois Correspondence](https://puremath.quantumdictionary.io/galois-correspondence-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

A bijective, order-reversing correspondence between intermediate fields of a finite Galois extension and subgroups of its Galois group, realized by mapping a subgroup to its fixed field and an intermediate field to the subgroup of automorphisms that fix it.

 

 

 

 

 





 

 



 ##  [Galois Correspondence](https://algebra.quantumdictionary.io/galois-correspondence-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

A bijective (order-reversing) correspondence between intermediate substructures of a field extension and subgroups of the extension's automorphism group, which identifies subfields fixed by subgroups with the subgroups themselves in the case of a Galois extension.