Solvable group

From Simple English Wikipedia, the free encyclopedia

In mathematics, a solvable group or soluble group is a group that is formed from by groups whose group operation is commutative.[1]

Relation with the order of the group[change | change source]

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[change | change source]

The definition of solvable groups show why the polynomial equations of degree greater than 5 are (in general) not solvable using finite arithmetic operations (Galois theory).

References[change | change source]

  1. Weisstein, Eric W. "Solvable Group". mathworld.wolfram.com. Retrieved 2022-11-03.