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.
A finiteness condition on the coefficients of the probabilistic zeta function
LUCCHINI, ANDREA
2013
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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IJGT_2013 Spring_Vol 2_Issue 1_Pages 167-174.pdf
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