Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function |
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Authors: | Andrea Lucchini |
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Institution: | (1) Muroran Institute of Technology, 27-1 Mizumoto, Muroran 050-8585, Japan |
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Abstract: | It has been conjectured by Mann that the infinite sum Σ
H
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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Keywords: | |
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