Fel'dman G. M.
Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 441-448
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.
Groups admitting a characterization of the Gaussian distribution by the equidistribution of a monomial and linear statistics
Ukr. Mat. Zh. - 1990. - 42, № 1. - pp. 139-142
Characterizing the Gaussian distribution on groups by the uniform distribution of a monomial and linear statistics
Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1112–1118