On layers in the system of generators of the subdirect product of subgroups of a finite group

We give a description of layers in the system of generators of the subdirect product of subgroups of a finite group and prove a formula for the corresponding length of the covering in terms of the subgroups of the finite group. On the base of these results we give a description of the behaviour of distributions of random variables in some particular cases of the linear autoregression scheme with random control on a finite group.