Central series

Central series of finite length
This is the default meaning of the term central series.

A subgroup series:

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

is termed a central series if it satisfies the following conditions:


 * 1) It is a normal series: every $$K_i$$ is normal in $$G$$
 * 2) For every $$i$$, $$K_i/K_{i+1}$$ is contained in the center of $$G/K_{i+1}$$.

Equivalently, it should satisfy the condition that for every $$i$$:

$$[G,K_i] \subset K_{i+1}$$

Stronger properties

 * Weaker than::Strongly central series

Weaker properties

 * Stronger than::Normal series:
 * Stronger than::Subnormal series