Supersolvable group
= Supersolvable group
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= Supersoluble group
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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, $A_4$ 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.