A supersolvable group is a type of group in the field of group theory, a branch of mathematics. A group \( G \) is said to be supersolvable if it has a normal series where each factor group is cyclic of prime order.
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A finite group is supersolvable if it has a normal series of a group whose nontrivial factors are cyclic of prime order. This is stronger than solubility, because the individual terms must be normal in the ambient group. For instance, is soluble via its normal Klein four-group, but is not supersolvable: it has no normal subgroup of order two or three with which such a series could begin.