##  [Galois Theory](/index.php/galois-theory) 

  ##  [Galois Theory](https://algebra.quantumdictionary.io/galois-theory-0) 

  

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

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The study of the relationship between field extensions and groups of field automorphisms that permute algebraic roots, giving a correspondence between intermediate fields and subgroups of an automorphism group, and linking solvability questions to group-theoretic properties.