Complex Euler’s Groups and Values of Euler’s Function at Complex Integer Gauss Points

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+0 i ) n : it is isomorphic to the product of three cyclic group or orders (8, 3 n −1 and 3 n −1 ).