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.
Non-prosoluble profinite groups with a rational probabilistic zeta function
DETOMI, ELOISA MICHELA;LUCCHINI, ANDREA
2007
Abstract
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.
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