Solvable Group


Considering the subgroup sequence of group , and that is a normal subgroup of , if is a commutative group (Abelian group), then is solvable group.

The symmetric group is solvable group if and not solvable group if .

Given a polynomial , let be the decomposition of with fixed field .
The Galois group is an isomorphism of the symmetric group .
Therefore, if , the general polynomial cannot be algebraically solved.

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