Sub-central factor of normalizer

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a sub-central factor of normalizer if there exists an ascending chain:

$$H = H_0 \le H_1 \le \ldots \le H_n = G$$

such that each $$H_i$$ is a central factor of normalizer of $$H_{i+1}$$.

Stronger properties

 * Weaker than::Central factor of normalizer
 * Weaker than::Central factor
 * Weaker than::Self-normalizing subgroup