On the universal and generalized orbifold Euler characteristics

We discuss the universal orbifold Euler characteristic and generalized orbifold Euler characteristics corresponding to finitely generated groups $A$ (the $A$-Euler characteristics). We show that the collection of all $A$-Euler characteristics for $A$ of the form $A^{\mathrm{\prime }}\times Z$ ($Z$ is the group of integers) with finite $A^{\mathrm{\prime }}$ determine the universal orbifold Euler characteristic.