It has been conjectured by Mann that the infinite sum ∑ μ(H,G)/|G:H|^ s , where H ranges over all open subgroups of a finitely generated profinite group G, converges absolutely in some half right plane if G is positively finitely generated. We prove that the conjecture is true if the nonabelian crowns of G have bounded rank. In particular Mann’s conjecture holds if G has polynomial subgroup growth or is an adelic profinite group.

Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function

LUCCHINI, ANDREA
2011

Abstract

It has been conjectured by Mann that the infinite sum ∑ μ(H,G)/|G:H|^ s , where H ranges over all open subgroups of a finitely generated profinite group G, converges absolutely in some half right plane if G is positively finitely generated. We prove that the conjecture is true if the nonabelian crowns of G have bounded rank. In particular Mann’s conjecture holds if G has polynomial subgroup growth or is an adelic profinite group.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/127697
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