On the lattice of subgroups of the lamplighter group

DOI10.1142/S0218196714500374zbMath1317.20032arXiv1203.5800MaRDI QIDQ2934269

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Publication date: 12 December 2014

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

Full work available at URL: https://arxiv.org/abs/1203.5800

zbMATH Keywords

subgroup growthlamplighter groupautomaton groupsprofinite groupsself-similar groupscongruence subgroup propertyrank gradientsMealey automatascale invariant groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Chains and lattices of subgroups, subnormal subgroups (20E15) Extensions, wreath products, and other compositions of groups (20E22) Groups acting on trees (20E08) Limits, profinite groups (20E18)

Related Items (13)

Affine automorphisms of rooted trees ⋮ Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups ⋮ From isolated subgroups to generic permutation representations ⋮ On Bohr compactifications and profinite completions of group extensions ⋮ The lamplighter group of rank two generated by a bireversible automaton ⋮ Invariant random subgroups of lamplighter groups ⋮ On the rigidity of rank gradient in a group of intermediate growth ⋮ From Self-Similar Groups to Self-Similar Sets and Spectra ⋮ Ranks of subgroups in boundedly generated groups ⋮ The Lamplighter Group ℤ₃≀ℤ Generated by a Bireversible Automaton ⋮ Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders ⋮ A language hierarchy and kitchens-type theorem for self-similar groups ⋮ On discrete homology of a free pro--group

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