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...

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

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

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 ∞ (...

then any group of order n is solvable. Burnside's theorem, proved using group characters, states that every group of order n is solvable when n is divisible...

the case n = 1. A group with G ( n ) ≠ { e } {\displaystyle G^{(n)}\neq \{e\}} for all n in N is called a non-solvable group. A group with G ( α ) = {...

By contrast, for a solvable group the definition requires each quotient to be abelian. In another direction, a polycyclic group must have a subnormal...

polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are...

quintics. A solvable quintic is thus an irreducible quintic polynomial whose roots may be expressed in terms of radicals. To characterize solvable quintics...