Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function.

DOI10.1007/S11856-011-0003-YzbMath1235.20028OpenAlexW1972629892MaRDI QIDQ532575

Andrea Lucchini

Publication date: 5 May 2011

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

Full work available at URL: https://doi.org/10.1007/s11856-011-0003-y

zbMATH Keywords

Möbius functionssubgroups of finite indexfinitely generated profinite groupsprobabilistic zeta functionsnonabelian crowns

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 (3)

The group of all finite-state automorphisms of a regular rooted tree has a minimal generating set. ⋮ Profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function. ⋮ Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function

Cites Work

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• Simple groups, maximal subgroups, and probabilistic aspects of profinite groups
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• Subgroup growth and congruence subgroups
• A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS
• On Product Partitions of Integers
• The X-Dirichlet polynomial of a finite group
• Maximal subgroups in finite and profinite groups
• Positively finitely generated groups
• Subgroups of solvable groups with non-zero Möbius function

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