I want to construct the elements Z0, Z1,...Zi of the upper central series
of a finite group G.
we have Z0(G)=1
Zi+1(G) / Zi(G) = Centre(G / Zi(G).
But how can I get Zi+1 from the last equation??
DirectProduct(Zi(G), Centre(G / Zi(G)) will not be isomorph to Zi+1 and a
SemidirectProduct between Zi(G) and Centre(G / Zi(G) does not exist.