Subgroups of solvable groups with non-zero Möbius function

DOI10.1515/JGT.2007.047zbMath1130.20027OpenAlexW2054912028MaRDI QIDQ5309025

Andrea Lucchini

Publication date: 9 October 2007

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

Full work available at URL: https://doi.org/10.1515/jgt.2007.047

zbMATH Keywords

finite solvable groupsMöbius functionssubgroups of finite indexzeta functionsfinitely generated profinite groupsnumbers of subgroupsprosolvable groupsrandom elements

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Subgroup theorems; subgroup growth (20E07) Series and lattices of subgroups (20D30) Generators, relations, and presentations of groups (20F05) Other Dirichlet series and zeta functions (11M41) Limits, profinite groups (20E18) Probabilistic methods in group theory (20P05)

Related Items (8)

Boolean lattices in finite alternating and symmetric groups ⋮ Intersections of maximal subgroups in prosolvable groups ⋮ On profinite groups with polynomially bounded Möbius numbers ⋮ Profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function. ⋮ Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function. ⋮ On the subgroups with non-trivial Möbius number ⋮ Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients

Cites Work

• A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS
• A Bound for the Number of Multiplicative Partitions
• The X-Dirichlet polynomial of a finite group
• Positively finitely generated groups
• On the Möbius function of a finite group

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