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.
Read more about Solvable Group: Definition, Examples, Properties, Burnside's Theorem
Famous quotes containing the words solvable and/or group:
“The problems of the world, AIDS, cancer, nuclear war, pollution, are, finally, no more solvable than the problem of a tree which has borne fruit: the apples are overripe and they are falling—what can be done?... Nothing can be done, and nothing needs to be done. Something is being done—the organism is preparing to rest.”
—David Mamet (b. 1947)
“Stripped of ethical rationalizations and philosophical pretensions, a crime is anything that a group in power chooses to prohibit.”
—Freda Adler (b. 1934)