AN UNCOUNTABLE FAMILY OF 3-GENERATED GROUPS WITH ISOMORPHIC PROFINITE COMPLETIONS

DOI10.1142/S0218196714500039zbMath1297.20029arXiv1303.5782MaRDI QIDQ5410738

Volodymyr V. Nekrashevych

Publication date: 17 April 2014

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

Full work available at URL: https://arxiv.org/abs/1303.5782

zbMATH Keywords

growth ratesprofinite completionsresidually finite groupsiterated monodromy groupsjust-infinite groupsgenera of groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Residual properties and generalizations; residually finite groups (20E26) Groups acting on trees (20E08) Limits, profinite groups (20E18)

Related Items (4)

Amenability and profinite completions of finitely generated groups ⋮ Torsion-free nilpotent groups of small Hirsch length with isomorphic finite quotients ⋮ Mating, paper folding, and an endomorphism of ℙℂ² ⋮ A topological zero-one law and elementary equivalence of finitely generated groups

Cites Work

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• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
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• A minimal Cantor set in the space of 3-generated groups.
• A group of non-uniform exponential growth locally isomorphic to $IMG(z^2+i)$
• DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
• Metabelian groups with the same finite quotients
• CONJUGATION IN TREE AUTOMORPHISM GROUPS

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