Relevant Courses: Math 493
The derived series or commutator series of a group is defined as follows:
- The zeroth member is the group itself.
- The member indexed by a successor ordinal is the commutator subgroup of its predecessor.
- The member indexed by a limit ordinal is the intersection of all previous members.
Solvable
A group is solvable if and only if its derived series terminates at the identity element.