Solvable GroupConsidering 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. [0]Top |