Residually solvable group

Symbol-free definition
A group is termed residually solvable if it satisfies the following equivalent conditions:


 * For every non-identity element in the group, there is a normal subgroup not containing that element, such that the quotient group is solvable
 * The derived series of the group reaches the identity element in countably many steps; in other words, the intersection of the (finite) members of the derived series is the trivial group