University of Isfahan International Journal of Group Theory 2251-7650 2 1 2013 03 01 A finiteness condition on the coefficients of the probabilistic zeta function 167 174 2760 10.22108/ijgt.2013.2760 EN Hoang Dung Duong Mathematisch Instituut, Leiden Universiteit, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands Andrea Lucchini Dipartimento di Matematica Università di Padova Journal Article 2012 12 22 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. Probabilistic zeta function finiteness conditions special linear groups https://ijgt.ui.ac.ir/article_2760_6ca06204ff8803a9692e43ba9bbb64d6.pdf