The significance of Galois extensions and Galois groups is that they allow a complete description of the intermediate fields : there is a bijection between the intermediate fields and the subgroups of the Galois group, described by the fundamental theorem of Galois theory.
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After much discussion, and a federal aid financial carrot of $ 47, 000 to provide intermediate fields suitable to military uses as well as to assist civil aviation resulted, on March 1941, in the transfer of the airport to the Mecosta County Airport committee for $ 1.
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This is almost immediate as a way of showing how Artin's result implies the classical result, and a bound for the number of exceptional " c " in terms of the number of intermediate fields results ( this number being something that can be bounded itself by Galois theory and " a priori " ).
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