Epicentral series

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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]

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).