### Abstract:

Let G be a group. The groups G
′
for which G is an automorphism group have
not been fully characterized. Suppose R is a Completely Primary finite Ring with Jacobson
Radical J such that J
2 = (0). In this case, the characteristic of R is p or p
2
and the group of
units R
∗ = Zpr−1 × (I + J) . The structure of R
∗
is well known, but its automorphism group
is not well documented. Given the group R
∗
, let Aut(R
∗
) denote the group of isomorphisms
φ : R
∗ → R
∗ with multiplication given by the composition of functions. The structure of the
automorphism groups of finite groups is intimately connected to the structure of the finite
groups themselves. In this note, we determine the structure of Aut(R
∗
) using well known
procedures and to this end, extend the results previously obtained in this area of research