TY  - JOUR
AU  - Olukayode, Ayinde S. 
AU  - Abiodun, Oyekan E. 
PY  - 2008
TI  - Fundamental Properties of the Galois Correspondence
JF  - Journal of Mathematics and Statistics
VL  - 4
IS  - 4
DO  - 10.3844/jmssp.2008.245.249
UR  - https://thescipub.com/abstract/jmssp.2008.245.249
AB  - Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn be the roots of f in K. Let G be embedded as a subgroup of the symmetric group ς. We determined the Galois group G, and the subgroup. Approach: computed some auxiliary polynomials that had roots in K, where the permutation of a set was considered distinct. The Galois Theory was deduced using the primitive element and Splitting theorems. Results:  The Galois extension K/L to identity L and its Galois group is a subgroup of G. which was referred to as the main theorem which we proved. Conclusion: Hence the findings suggest the need for computing more auxiliary polynomials that have roots.