solvable group

English

Noun

solvable group (plural solvable groups)

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

Hyponyms

• abelian group

Further reading

• Subgroup series § Normal series, subnormal series on Wikipedia.Wikipedia