Trellis properties of group codes

In this paper, we discuss some trellis properties for codes over finite Abelian groups, and prove that for any biproper p-basis of a group code, their atomic spans and orders of the first and last nonzero components of vectors in the biproper p-basis are unique. This is the generalization of the corresponding trellis property for a linear code over a field. We also discuss difficulties when we try to generalize the theory of a tail-biting trellis over a field into that of a tail-biting trellis over a finite Abelian group.