Strongly central series

Definition
A subgroup series

$$G = K_1 \ge K_2 \ge K_3 \ge \ldots \ge K_c \ge K_{c+1} = 1$$

is termed strongly central if $$[K_i,K_j] \le K_{i+j}$$ for every $$i,j = 1,2,\ldots,c$$.

(A similar definition works for transfinite series).

Examples
The lower central series and upper central series of a nilpotent group are both examples of strongly central series.

Weaker properties

 * Stronger than::Normal series:
 * Stronger than::Central series:

Textbook references

 * , Page 76, Section 3.2 (formal definition, around equation 3.2.5)