What is Solvable group?
In [[mathematics]], a '''solvable group''' or '''soluble group''' is a [[Group (mathematics)|group]] which has a [[Subgroup series|subnormal series]] with [[Abelian group|abelian]] factors. == Relation with the order of the group == {{Main article|Order (group theory)}} The Feit-Thompson theorem says that every group of odd order is solvable. Every finite group of order 60 or greater, every [[abelian group]], and every subgroup of a solvable group is solvable. == Applications == The definition of solvable groups show why the polynomial equations of [[Degree (mathematics)|degree]] greater than 5 are (in general) not solvable using finite arithmetic operations ([[Galois theory]]). == References == <references /> [[Category:Group theory]]