Dimension and randomness in groups acting on rooted trees

DOI10.1090/S0894-0347-04-00467-9zbMath1135.20015arXivmath/0212191OpenAlexW2114619383MaRDI QIDQ3155915

Miklós Abért, Bálint Virág

Publication date: 4 January 2005

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0212191

zbMATH Keywords

finitely generated subgroupsgroups acting on treesdense free subgroups\(p\)-adic automorphism groupsasymptotic orders of elementsdimension theory of groups

Mathematics Subject Classification ID

Trees (05C05) Subgroup theorems; subgroup growth (20E07) Asymptotic properties of groups (20F69) Hausdorff and packing measures (28A78) Groups acting on trees (20E08) Limits, profinite groups (20E18)

Related Items (30)

The finitely generated Hausdorff spectra of a family of pro-\(p\) groups ⋮ Hausdorff dimension in a family of self-similar groups. ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map ⋮ Strong approximation in random towers of graphs. ⋮ A pro‐pgroup with full normal Hausdorff spectra ⋮ Hausdorff dimensions in \(p\)-adic analytic groups ⋮ On arboreal Galois representations of rational functions ⋮ Hausdorff dimension of some groups acting on the binary tree ⋮ Some topics in the dynamics of group actions on rooted trees. ⋮ GGS-groups: Order of congruence quotients and Hausdorff dimension ⋮ Dynamical properties of profinite actions ⋮ Branch rings, thinned rings, tree enveloping rings. ⋮ Hausdorff dimension in \(R\)-analytic profinite groups ⋮ Free subgroups in groups acting on rooted trees ⋮ Rank gradient, cost of groups and the rank versus Heegaard genus problem ⋮ On the girth of random Cayley graphs ⋮ FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION ⋮ On the commensurator of the Nottingham group ⋮ Isometry types of profinite groups. ⋮ Automorphisms of restricted parabolic trees and Sylow \(p\)-subgroups of the finitary symmetric group ⋮ Hausdorff dimension of the second Grigorchuk group ⋮ Most actions on regular trees are almost free. ⋮ Generic groups acting on regular trees ⋮ The congruence subgroup problem for a family of branch groups ⋮ A pro-\(p\) group with infinite normal Hausdorff spectra ⋮ Spinal groups: semidirect product decompositions and Hausdorff dimension ⋮ Hereditarily just infinite profinite groups with complete Hausdorff dimension spectrum ⋮ Amenable actions, free products and a fixed point property ⋮ On Subgroups of the Nottingham Group of Positive Hausdorff Dimension

Cites Work

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• Limit distributions for minimal displacement of branching random walks
• The order of elements in Sylow \(p\)-subgroups of the symmetric group.
• Postulates for subadditive processes
• Graded subalgebras of affine Kac-Moody algebras
• A non-abelian free pro-\(p\) group is not linear over a local field
• Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity.
• New horizons in pro-\(p\) groups
• Profinite groups admitting just infinite quotients
• Eigenvalues of random wreath products
• The ubiquity of free subgroups in certain inverse limits of groups
• The entropy of graded algebras
• Finitely generated profinitely dense free groups in higher rank semi-simple groups
• Residual properties of groups and probabilistic methods
• GENERATING TRANSITIVE PERMUTATION GROUPS
• Chernoff's theorem in the branching random walk
• Subgroups and subrings of profinite rings
• Hausdorff dimension, pro-𝑝 groups, and Kac-Moody algebras
• CONJUGATION IN TREE AUTOMORPHISM GROUPS
• On some problems of a statistical group-theory. I
• The probability of generating the symmetric group

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