Epicentral series

Definition

The epicentral series (sometimes also called the upper epicentral series) of a group is an ascending series defined as follows. $Z_{0}^{*}(G)$ is the trivial subgroup, and for a positive integer $i$, $Z_{i}^{*}(G)$ is PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

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In particular, $Z_{1}^{*}(G)=Z^{*}(G)$ is the epicenter of $G$. Note, however, that the epicentral series does not satisfy $Z^{*}(G/Z_{i-1}^{*}(G))=Z_{i}^{*}(G)/Z_{i-1}^{*}(G)$.