Galois Group Correspondence On Extension Fields Over Q

  • Novita Dahoklory Pattimura University
  • Henry W. M. Patty Pattimura University
Keywords: Extension fields, Galois extension, Galois correspondence


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 .



Download data is not yet available.


Dummit, Abstract Algebra Dummit and Foote.pdf. 1999.

Khanna, Vijay K. Khanna, S.K. Bhamri - A Course in Abstract Algebra-Vikas (2013).pdf., 2000.

Lidl, R., & Niederreiter, H., Introduction to finite fields and their applications. Cambridge: Cambridge University Press., 1986.

Malik, D. S., & Mordeson, J. N. MTH 581-582 Introduction to Abstract Algebra. America, February., 2007.

Morandi, P., Fields and Galois Theory. New York: Springer., 1999.

Roman, S., Advanced Linear Algebra. New York: Springer, 2005

How to Cite
Dahoklory, N., & Patty, H. W. M. (2023). Galois Group Correspondence On Extension Fields Over Q. Pattimura Proceeding: Conference of Science and Technology, 4(1), 17-28. Retrieved from