On the subgroups with non-trivial Möbius number

DOI10.1515/JGT.2010.009zbMath1206.20032MaRDI QIDQ3584491

Andrea Lucchini

Publication date: 30 August 2010

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

zbMATH Keywords

Möbius functionsubgroups of finite indexfinitely generated profinite groupsmonolithic groupslattices of open subgroups

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 (8)

On subgroups with non-zero Möbius numbers in the alternating and symmetric groups. ⋮ A closure operator on the subgroup lattice of \(\operatorname{GL}(n, q)\) and \(\operatorname{PGL}(n, q)\) in relation to the zeros of the Möbius function ⋮ On profinite groups with polynomially bounded Möbius numbers ⋮ On two Möbius functions for a finite non-solvable group ⋮ Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function ⋮ The Möbius function of PSL(3,2p) for any prime p ⋮ The Möbius function of PSU(3, 2^{2^n}) ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients

Cites Work

• Simple groups, maximal subgroups, and probabilistic aspects of profinite groups
• Subgroups of prime power index in a simple group
• On the Möbius number of the subgroup lattice of the symmetric group
• The probability of generating a finite classical group
• A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS
• On Product Partitions of Integers
• The X-Dirichlet polynomial of a finite group
• Positively finitely generated groups
• Subgroups of solvable groups with non-zero Möbius function

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