In mathematics, solvable may refer to: * Solvable group, a group that can be constructed by compositions of abelian groups, or equivalently a group whose derived series reaches the trivial group in finitely many steps *

Solvable extension In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvabl ...

, a field extension whose Galois group is a solvable group *Solvable equation, a polynomial equation whose Galois group is solvable, or equivalently, one whose solutions may be expressed by

nested radical In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include :\sqrt, which arises in discussing the regular pentagon, and more co ...

s * Solvable Lie algebra, a Lie algebra whose derived series reaches the zero algebra in finitely many steps *

Solvable problem In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm wheth ...

, a computational problem that can be solved by a Turing machine *

Exactly solvable model In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...

in statistical mechanics, a system whose solution can be expressed in closed form, or alternatively, another name for completely integrable systems

See also