Книга: Solvable group: Mathematics, Group Theory, Abelian Group, Group Extension, Commutator Subgroup, Trivial Group, Galois Theory, Polynomial, Galois Group, Subgroup Series, Normal Subgroup

High Quality Content by WIKIPEDIA articles! In mathematics, more specifically in the field of group theory, a solvable group (or soluble group) is a group that can be constructed from abelian groups using extensions. That is, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word 'solvable' arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable by radicals if and only if the corresponding Galois group is solvable.