In mathematics, solvable may refer to: *

Solvable group 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. Equivalently, a solvable group is a group whose derived series terminat ...

, 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, a field extension whose Galois group is a solvable group *Solvable equation, a

polynomial equation In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0, where ''P'' is a polynomial with coefficients in some field (mathematics), field, often the field of the rational numbers. For example, x^5-3x+1=0 is a ...

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 pentagon, regular pentagon, an ...

s *

Solvable Lie algebra In mathematics, a Lie algebra \mathfrak is solvable if its derived series terminates in the zero subalgebra. The ''derived Lie algebra'' of the Lie algebra \mathfrak is the subalgebra of \mathfrak, denoted : mathfrak,\mathfrak/math> that consist ...

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

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

See also