Probabilistic zeta functions of subgroup functors / I. P. Kramarev. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 1. P. 20-23 [Moscow Univ. Math. Bulletin. Vol. 64, N 1, 2009. P. 20-23].
A probabilistic zeta function of a finite group is generalized by using the notion of a group functor. Factorization properties of this function as a Dirichlet polynomial are studied and an example of the simplest subgroup functor associating a group with the set of its normal subgroups is considered.