Finiteness of profinite groups with a rational probabilistic zeta function

TL;DR

This paper proves that certain profinite groups with a rational probabilistic zeta function have finitely many maximal subgroups, revealing a structural finiteness property related to their zeta functions.

Contribution

It establishes a new link between the rationality of the probabilistic zeta function and the finiteness of maximal subgroups in specific profinite groups.

Findings

Profinite groups with rational probabilistic zeta functions have finitely many maximal subgroups.

The result applies to a particular class of profinite groups.

It advances understanding of the relationship between zeta functions and group structure.

Abstract

We prove that every profinite group in a certain class with a rational probabilistic zeta function has only finitely many maximal subgroups.