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 \(A'\times Z\) (\(Z\) is the group of integers) with finite \(A'\) determine the universal orbifold Euler characteristic.