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Line 21: == Structure of Galois groups == === Fundamental theorem of Galois theory === One of the important structure theorems from Galois theory comes from the [[fundamental theorem of Galois theory]]. This states that given a finite Galois extension <math>K/k</math>, if there is a bijection between the set of subfields <math>k \subset E \subset K</math> and the subgroups <math>H \subset G.</math> Then, <math>E</math> is given by the set of invariants of <math>K</math> under the action of <math>H</math>, so :<math>E = K^H = \{ a\in K : ga = a \text{ where } g \in H \}</math>

Galois group: Difference between revisions