%0 Journal Article
%T A finiteness condition on the coefficients of the probabilistic zeta function
%A Hoang Dung Duong
%A Andrea Lucchini
%J International Journal of Group Theory
%D 2013
%I University of Isfahan
%X We discuss whether finiteness properties of a profinite group $G$ can be deduced from the coefficients of the probabilisticzeta 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.
%K Probabilistic zeta function
%K finiteness conditions
%K special linear groups
%U http://www.theoryofgroups.ir/?_action=showPDF&article=2760&_ob=6ca06204ff8803a9692e43ba9bbb64d6&fileName=full_text.pdf.