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

Abstract

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