Supersolvable group
= Supersolvable group
{wiki}
= Supersoluble group
{synonym}
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.