Finite characteristic series operator

Definition with symbols
The finite characteristic series operator is a group property modifier that takes as input a group property $$p$$ and outputs a group property $$q$$ such that a group $$G$$ satisfies $$q$$ if and only if it has a characteristic series $$e = H_0 \le H_1 \le \ldots \le H_r = G$$ such that each quotient $$H_i/H_{i-1}$$ satisfies property $$p$$.

Weaker modifiers

 * Finite normal series operator
 * Poly operator