Seminario Dottorato: Moebius function and probabilistic zeta function associated to a group

Wednesday 24 February 2010 - Valentina Colombo

ARGOMENTI: Seminari Dottorato

Wednesday 24 February 2010 h. 15:00, room 2BC/60
Valentina Colombo (Padova, Dip. Mat.)
"Moebius function and probabilistic zeta function associated to a group"

Many authors have studied the probabilistic zeta function associated to a finite group; in the last years the study has been extended to profinite groups. To understand how the probabilistic zeta function is defined, it is necessary to introduce another function associated to a group: the Moebius function. We will start considering finite groups: we will explain how these two functions are obtained and we will give some basic examples. Then we will define the profinite groups and proceed to investigate whether and how a probabilistic zeta function can be associated to them. This is not always possible: Mann has conjectured that for a particular class of profinite groups (PFG groups) the definition of this function makes sense. We will present some recent results which suggest that the conjecture is true.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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