Structure results for transitive, untwisted, superlinked finite covers

Abstract

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.