Hoang Dung Duong - Mathematisch Instituut, Leiden Universiteit, Niels Bohrweg ۱, ۲۳۳۳ CA Leiden, The Netherlands
Andrea Lucchini - Dipartimento di Matematica Università di Padova

We discuss whether finiteness properties of a profinite group G can be deduced from the coefficients of the probabilistic‎ ‎zeta function P_G(s)‎. ‎In particular we prove that if P_G(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(۲,p) for some prime p‎, ‎then G contains only finitely many maximal subgroups‎.

Probabilistic zeta function, finiteness conditions, special linear groups