We investigate the structure of transitive, untwisted, superlinked finite covers whose kernels are central in their automorphism groups. We introduce the concept of an $n$-conjugate system for a pair $(W,K)$, where $W$ is a permutation structure, $K$ is a finite abelian group and $n\in\omega+1$. This concept allows us to characterize the given class of finite covers for structures $W$ which satisfy a certain connectedness condition; further, the irreducibility of such a cover is equivalent to a simple condition on a corresponding $n$-conjugate system. Finally, we consider structures with strong types, for which there is a much simpler characterization.

1991 Mathematics Subject Classification: 03C35, 20B27.