A PROBABILISTIC GENERALIZATION OF SUBNORMALITY

A subnormal subgroup X of G has the following property: there exists a Dirichlet polynomial Q(s) with integer coefficients such that, for each t ∈ ℕ, Q(t) is the conditional probability that t random elements generate G given that they generate G together with the elements of X In this paper we analyze how far can a subgroup X be with this property from being a subnormal subgroup.