Explore: Solvable Groups

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

of a solvable group in group theory allows one to determine whether a polynomial is solvable in radicals, depending on whether its Galois group has the

theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence

Look up solvable in Wiktionary, the free dictionary. In mathematics, solvable may refer to: Solvable group, a group that can be constructed by compositions

Divide and conquer breaking down a large, complex problem into smaller, solvable problems Help-seeking obtaining external assistance to deal with obstacles

algebras are analogs of solvable groups. Any nilpotent Lie algebra is a fortiori solvable but the converse is not true. The solvable Lie algebras and the

subgroup in concept and notation is the solvable radical. The solvable radical is defined to be the largest solvable normal subgroup, and is denoted O ∞ (

of its Galois group for expressing this characterization in terms of solvable groups; the proof that the symmetric group is not solvable if its degree

property: finite groups, periodic groups, simple groups, solvable groups, and so on. Rather than exploring properties of an individual group, one seeks to

groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups.