Saturday, 20 January 2018

Given a tower of field extensions, does this equality involving Galois group orders hold in general?

Suppose we have a tower of field extensions:



¯FKEF



Is it true in general that |G(K/F)|=|G(K/E)||G(E/F)|?



I was able to verify some specific examples, like Q(32,ω) for x32 and another extension, but how could I show that this holds in general for all such towers of extensions?

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