Jennings series

Definition
Suppose $$p$$ is a prime number and $$G$$ is a finite p-group. The Jennings series of $$G$$ is defined as a descending series $$\kappa_n(G), n \in \mathbb{N}$$, where:


 * $$\kappa_1(G) = G$$
 * $$\kappa_{n+1}(G) = [G,\kappa_n(G)]\mho^1(\kappa_i(G))$$

where $$i = \lceil n/p \rceil$$

Here, $$\mho^1(\kappa_i(G))$$ is the agemo subgroup -- the subgroup generated by the $$p^{th}$$ powers of elements in $$\kappa_i(G)$$.

This is an example of a descending central series, albeit one that descends more slowly than the lower central series, and in fact, even more slowly than the lower exponent-p central series.