Research Article Open Access

Fundamental Properties of the Galois Correspondence

Ayinde S. Olukayode and Oyekan E. Abiodun

Abstract

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.

Journal of Mathematics and Statistics
Volume 4 No. 4, 2008, 245-249

DOI: https://doi.org/10.3844/jmssp.2008.245.249

Submitted On: 12 June 2008 Published On: 31 December 2008

How to Cite: Olukayode, A. S. & Abiodun, O. E. (2008). Fundamental Properties of the Galois Correspondence. Journal of Mathematics and Statistics, 4(4), 245-249. https://doi.org/10.3844/jmssp.2008.245.249

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Keywords

  • Splitting fields
  • symmetric group
  • galois group and theory
  • resolvents