A finiteness condition on the coefficients of the probabilistic zeta function

Document Type: Ischia Group Theory 2012

Authors

1 Mathematisch Instituut, Leiden Universiteit, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

2 Dipartimento di Matematica Università di Padova

Abstract

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 $PSL(2,p)$ for some prime $p$‎, ‎then $G$ contains only finitely many maximal subgroups‎.

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