solvable group

noun

A group G which is part of a finite chain Gᵢ (0 ≤ i ≤ n) of subgroups, where G₀ is the trivial subgroup and Gₙ = G, such that each intermediate subgroup Gᵢ is a normal subgroup of the next in the chain (i.e., Gᵢ ◁ Gᵢ₊₁) and each quotient Gᵢ₊₁/Gᵢ is a cyclic group.

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Meanings

nounsolvable group (plural solvable groups)

plural solvable groups

  1. Galois theoryalgebraA group G which is part of a finite chain Gᵢ (0 ≤ i ≤ n) of subgroups, where G₀ is the trivial subgroup and Gₙ = G, such that each intermediate subgroup Gᵢ is a normal subgroup of the next in the chain (i.e., Gᵢ ◁ Gᵢ₊₁) and each quotient Gᵢ₊₁/Gᵢ is a cyclic group.
Cite this entry
APA

solvable group. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/solvable%20group

MLA

“solvable group.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/solvable%20group. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “solvable group,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/solvable%20group.

Source: solvable group on Wiktionary, CC BY-SA 4.0.