I-centerless IAPS

Definition
An IAPS of groups $$(G,\Phi)$$ is said to be i-centerless if there is no sub-IAPS $$H$$ for which $$H_n \le Z(G_n)$$ for every $$n$$. Here $$Z(G_n)$$ denotes the center of $$G_n$$.

Stronger properties

 * non-Abelian i-simple IAPS