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AUTOMORPHISMS OF THE UNIT GROUPS OF SQUARE RADICAL ZERO FINITE COMMUTATIVE COMPLETELY PRIMARY RINGS

2016
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International Journal of Pure and Applied Mathematics
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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

doi:10.12732/ijpam.v108i1.6
fatcat:4lychbfhgbghroua2i5qipbajm