A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS

DOI10.1142/S0218196705002633zbMath1098.20025MaRDI QIDQ3379483

Avinoam Mann

Publication date: 6 April 2006

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

zbMATH Keywords

maximal subgroupscompletionsarithmetic groupsprofinite groupsprobabilistic zeta functionscongruence subgroup propertyPFG groupspositively finitely generated profinite groupsmaximal subgroup growth

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) 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 (12)

Subgroups of solvable groups with non-zero Möbius function ⋮ 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 ⋮ On the probability of generating prosoluble groups. ⋮ Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function. ⋮ On the subgroups with non-trivial Möbius number ⋮ Non-prosoluble 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
• Finite index subgroups in profinite groups.
• Subgroup growth and congruence subgroups
• On Product Partitions of Integers
• Maximal subgroups in finite and profinite groups

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