On profinite groups with polynomially bounded Möbius numbers

DOI10.1515/JGT.2010.050zbMath1228.20026OpenAlexW2025337173MaRDI QIDQ3007961

Andrea Lucchini

Publication date: 17 June 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgt.2010.050

zbMATH Keywords

Möbius functionsubgroups of finite indexfinitely generated profinite groupsalmost simple groupsprofinite groupsmonolithic groupspositively finitely generated groupsopen subgroupssubgroup theorems

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Other Dirichlet series and zeta functions (11M41) Chains and lattices of subgroups, subnormal subgroups (20E15) Limits, profinite groups (20E18) Probabilistic methods in group theory (20P05)

Related Items (2)

Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients

Cites Work

• On subgroups with non-zero Möbius numbers in the alternating and symmetric groups.
• Simple groups, maximal subgroups, and probabilistic aspects of profinite groups
• Complements of the socle in monolithic groups.
• A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS
• On the subgroups with non-trivial Möbius number
• Positively finitely generated groups
• Subgroups of solvable groups with non-zero Möbius function
• COEFFICIENTS OF THE PROBABILISTIC FUNCTION OF A MONOLITHIC GROUP
• THE EULERIAN FUNCTIONS OF A GROUP

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