Abstract
Let R be a finite commutative chain ring with invariants p, n, r, k, m. The purpose of this article is to study j-diagrams for the one group H = 1 + J(R) of R, where J(R) = (p) is Jacobson radical of R. In particular, we prove the existence and uniqueness of j-diagrams for such one group. These j-diagrams help us to solve several problems related to chain rings such as the structure of their unit groups and a group of all symmetries of {p(k')}, where k' | k. The invariants p, n, r, k, m and the Eisenstein polynomial by which R is constructed over its Galois subring determine fully the j-diagram for H.