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  "body": "\n## Summary\n\nA supersolvable group is a group with a finite chain of normal subgroups, all normal in the whole group, whose successive quotients are cyclic.\nThe condition is stronger than solvability and weaker than nilpotency for finite groups.\nSupersolvable groups share many good properties of nilpotent groups, and they appear naturally in the study of finite solvable groups and their representations.\n\n## Explanations\n\n### L1 human\n\nA solvable group can be built from abelian layers.\nA supersolvable group can be built from cyclic layers, and each partial stack of layers is normal in the whole group.\nThe symmetric group $S_3$ is supersolvable: it has the normal subgroup $A_3$, which is cyclic of order $3$, and the quotient $S_3/A_3$ is cyclic of order $2$.\nThe alternating group $A_4$ is solvable but not supersolvable.\n",
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