Field Theory: We define the Galois group of a polynomial g(x) as the group of automorphisms of the splitting field K that fix the base field F pointwise. The Galois group acts faithfully on the set of roots of g(x) and is isomorphic to a subgroup of a symmetric group. We also show that this action is transitive when g(x) is irreducible over F.
Tagged under: mathematics,field,theory,ring,galois,abstract,algebra,automorphism,cyclotomic,polynomial,root,extension,separable,algebraic,multiple,group,action,transitive,orbit,unity,primitive
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