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Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.

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In Galois theory, why solvable groups must have their quotient groups be Abelian? [closed]

The definition of solvable groups can be regarded as two constraints, one is that there must be a sequence of normal subgroups, and the other is that the quotient groups between these sequences are Ab …