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In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability is stronger than the notion of solvability. ==Definition== Let ''G'' be a group. ''G'' is supersolvable if there exists a normal series : such that each quotient group is cyclic and each is normal in . By contrast, for a solvable group the definition requires each quotient to be abelian. In another direction, a polycyclic group must have a normal series with each quotient cyclic, but there is no requirement that each be normal in . As every finite solvable group is polycyclic, this can be seen as one of the key differences between the definitions. For a concrete example, the alternating group on four points, , is solvable but not supersolvable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Supersolvable group」の詳細全文を読む スポンサード リンク
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