Galois Group Correspondence On Extension Fields Over Q

Abstract

Let be an extension field where denotes dimension of as a vector space over . Let be the group of all automorphism of that fixes where the order of is denoted by . Particularly, an extension field is called a Galois extension if . Moreover, we will give some properties of an extension field which is a Galois extension. Using the properties of Galois extension, we will show that there is an one-one correspondence between the set of all intermediate fields in and the set of all subgroups in . Furthermore, we will give some examples of Galois group correspondence using an extension field over .