Duong, H., Lucchini, A. (2013). A finiteness condition on the coefficients of the probabilistic zeta function. International Journal of Group Theory, 2(1), 167-174. doi: 10.22108/ijgt.2013.2760

Hoang Dung Duong; Andrea Lucchini. "A finiteness condition on the coefficients of the probabilistic zeta function". International Journal of Group Theory, 2, 1, 2013, 167-174. doi: 10.22108/ijgt.2013.2760

Duong, H., Lucchini, A. (2013). 'A finiteness condition on the coefficients of the probabilistic zeta function', International Journal of Group Theory, 2(1), pp. 167-174. doi: 10.22108/ijgt.2013.2760

Duong, H., Lucchini, A. A finiteness condition on the coefficients of the probabilistic zeta function. International Journal of Group Theory, 2013; 2(1): 167-174. doi: 10.22108/ijgt.2013.2760

A finiteness condition on the coefficients of the probabilistic zeta function

^{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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