The Probabilistic Zeta Function of Alternating and Symmetric Groups

DOI10.1142/S1005386709000200zbMath1189.20018OpenAlexW2020225599MaRDI QIDQ3633818

Marilena Massa, Andrea Lucchini

Publication date: 23 June 2009

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1005386709000200

zbMATH Keywords

symmetric groupsfinite simple groupsalternating groupsDirichlet seriesMöbius inversionsubgroup latticesrandom elementsDirichlet polynomialsprobabilistic zeta functions

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Other Dirichlet series and zeta functions (11M41) Simple groups: alternating groups and groups of Lie type (20D06) Subgroups of symmetric groups (20B35) Probabilistic methods in group theory (20P05)

Related Items (4)

Recognizing the characteristic of a simple group of Lie type from its probabilistic zeta function. ⋮ The coset poset and probabilistic zeta function of a finite group ⋮ The probabilistic zeta function of \(\text{PSL}(2,q)\), of the Suzuki groups \(^2B_2(q)\) and of the Ree groups \(^2G_2(q)\). ⋮ Profinite groups with a rational probabilistic zeta function

Cites Work

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• Subgroups of prime power index in a simple group
• On the probabilistic zeta function for finite groups
• Crowns and factorization of the probabilistic zeta function of a finite group.
• The coset poset and probabilistic zeta function of a finite group
• The probabilistic zeta function of finite simple groups.
• The Sylow 2-subgroups of the finite classical groups
• RECOGNIZING THE ALTERNATING GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTION
• Finite Groups withp-Multiplicative Probabilistic Zeta Function

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