solvable group
Fetched 2026-10-26 (cache).
Synonyms: soluble group
Antonyms: soluble group
Related words from Datamuse; suggestions, not definitions.
Noun
- {{lb|en|algebra|Galois theory}} A group ''G'' which is part of a finite chain ''G<sub>i</sub>'' (0 ≤ ''i'' ≤ ''n'') of [[subgroup]]s, where ''G<sub>0</sub>'' is the [[trivial group|trivial subgroup]] and ''G<sub>n</sub> = G'', such that each intermediate subgroup ''G<sub>i</sub>'' is a [[normal subgroup]] of the next in the chain (i.e., ''G<sub>i</sub>'' ◁ ''G<sub>i+1</sub>'') and each [[quotient group|quotient]] ''G<sub>i+1</sub>/G<sub>i</sub>'' is a [[cyclic group]].
Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.