If there exists a one-to-one correspondence between two subgroups and subfields such that
then 
is said to have a Galois theory.
A Galois correspondence can also be defined for more general categories.
See also
Abel's Impossibility Theorem, Subfield
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References
Artin, E. Galois Theory, 2nd ed. Notre Dame, IN: Edwards Brothers, 1944.Birkhoff, G. and Mac Lane, S. "Galois Theory." Ch. 15 in A Survey of Modern Algebra, 5th ed. New York: Macmillan, pp. 395-421, 1996.Dummit, D. S. and Foote, R. M. "Galois Theory." Ch. 14 in Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 471-570, 1998.Stewart, I. Galois Theory. London: Chapman and Hall, London, 1972.
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Cite this as:
Weisstein, Eric W. "Galois Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GaloisTheory.html