The probabilistic zeta function of \(\text{PSL}(2,q)\), of the Suzuki groups \(^2B_2(q)\) and of the Ree groups \(^2G_2(q)\).

DOI10.2140/pjm.2009.240.185zbMath1167.20013OpenAlexW2052691508MaRDI QIDQ1011627

Publication date: 8 April 2009

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2009.240.185

zbMATH Keywords

Möbius function finite groups Suzuki groups subgroup lattices Dirichlet polynomials Ree groups probabilistic zeta functions coset posets simple groups of Lie type

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Maximal subgroups (20E28) Series and lattices of subgroups (20D30) Other Dirichlet series and zeta functions (11M41) Simple groups: alternating groups and groups of Lie type (20D06) Probabilistic methods in group theory (20P05)

Related Items (9)

Order complexes of coset posets of finite groups are not contractible. ⋮ On the (non-)contractibility of the order complex of the coset poset of an alternating group. ⋮ Recognizing the characteristic of a simple group of Lie type from its probabilistic zeta function. ⋮ Boolean lattices in finite alternating and symmetric groups ⋮ On the (non-)contractibility of the order complex of the coset poset of a classical group. ⋮ Profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function. ⋮ On the irreducibility of the Dirichlet polynomial of a simple group of Lie type. ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients ⋮ Recognizing \(\mathrm{PSL}(2,p)\) in the non-Frattini chief factors of finite groups.

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