Independent Linear Statistics on Finite Abelian Groups - Graczyk, P.; Fel'dman, G. M. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents.