Non-prosoluble profinite groups with a rational probabilistic zeta function
Eloisa Detomi, Andrea Lucchini · Journal of Group Theory · 2007
We discuss finiteness properties of a profinite group G whose probabilistic zeta function P G ( s ) is rational. In particular we prove that if P G ( s ) is rational and G has a finite number of non-alternating and non-abelian composition factors in a given composition series, then G /Frat( G ) is finite.