KnowraSolvable groupLinked fromLinked fromThe 8 pages that link to Solvable group, each with the reason it gives.All 8Broader topic 1Related 5Compared with 2Évariste GaloisRelated: Solvability of the Galois group characterizes equations solvable by radicals.Simple groupCompared with: Nonabelian simple groups obstruct solvability, while prime-order simple groups are solvable.Composition seriesRelated: A finite group is solvable exactly when all its composition factors are cyclic of prime order.Finite simple groupCompared with: Finite simple groups distinguish the solvable case from groups with nonsolvable composition factors.Abel–Ruffini theoremRelated: A polynomial is solvable by radicals when its Galois group is solvable.Solvability by radicalsRelated: A polynomial is solvable by radicals exactly when its Galois group is solvable, in characteristic zero.Tits alternativeBroader topic: Solvability defines the structured side of the theorem’s dichotomy.Feit–Thompson theoremRelated: Solvability is the conclusion guaranteed for every group in the theorem.