Profinite groups with a rational probabilistic zeta function
Eloisa Detomi, Andrea Lucchini · Journal of Group Theory · 2006
We discuss whether finiteness properties of a profinite group G can be deduced from the probabilistic zeta function P G ( s ). In particular we prove that in the prosoluble case, if P G ( s ) is rational then G /Frat( G ) is finite.