Abstract
To a finitely generated profinite group [Formula: see text], a formal Dirichlet series [Formula: see text] is associated, where [Formula: see text] and [Formula: see text] denotes the Möbius function of the lattice of open subgroups of [Formula: see text] Its formal inverse [Formula: see text] is the probabilistic zeta function of [Formula: see text]. When [Formula: see text] is prosoluble, every coefficient of [Formula: see text] is nonnegative. In this paper we discuss the general case and we produce a non-prosoluble finitely generated group with the same property.
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