Complex Euler’s groups and values of Euler’s function at complex integer Gauss points

摘要

The complex Euler group is defined associating to an integer complex number z the multiplicative group of the complex integers residues modulo z, relatively prime to z. This group is calculated for z = (3 + Oi)~n: it is isomorphic to the product of three cyclic group or orders (8, 3~(n-1) and 3~(n-1)).