Automorphisms of the unit groups of power four radical zero finite commutative completely rimary Rings

Abstract

Let G be a group. The groups G 0 for which G is an automorphism group have not been fully characterized. Suppose R is a class of power four radical zero finite commutative completely primary ring and J its Jacobson Radical, the structure of R∗ , the unit groups of R is precisely known, but the automorphisms of these unit groups is unknown. In this paper, we discover the structure and order of these automorphisms for all the characteristics of the ring R.