On the automorphism group of the one-rooted binary tree

DOI10.1006/JABR.1997.7033zbMath0902.20017OpenAlexW2002892803MaRDI QIDQ1372656

J. Ning

Publication date: 7 January 1998

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7033

zbMATH Keywords

endomorphismsautomorphism groupsisometry groupsBurnside groupsfree monoidsfinite-state automataiterated wreath productsfinite-state automorphismsfunctionally recursive automorphismsregular binary trees

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Algebraic theory of languages and automata (68Q70) Automorphisms of infinite groups (20E36) Extensions, wreath products, and other compositions of groups (20E22) Automorphism groups of groups (20F28) Representations of groups as automorphism groups of algebraic systems (20F29) Infinite automorphism groups (20B27)

Related Items (15)

CONJUGATION IN TREE AUTOMORPHISM GROUPS ⋮ The group of all finite-state automorphisms of a regular rooted tree has a minimal generating set. ⋮ Affine automorphisms of rooted trees ⋮ Functionally recursive rings of matrices -- two examples ⋮ Settled elements in profinite groups ⋮ Lie algebra associated with the group of finitary automorphisms of \(p\)-adic tree. ⋮ The automorphism tower of groups acting on rooted trees ⋮ Conjugacy classes of the automorphism group of a tree ⋮ Extensions of automorphisms of self-similar groups ⋮ Abelian state-closed subgroups of automorphisms of \(m\)-ary trees. ⋮ A just-nonsolvable torsion-free group defined on the binary tree ⋮ A language hierarchy and kitchens-type theorem for self-similar groups ⋮ Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity. ⋮ The word and order problems for self-similar and automata groups ⋮ Wreath operations in the group of automorphisms of the binary tree

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• On Burnside's problem on periodic groups
• On a 2-generated infinite 3-group: Subgroups and automorphisms
• Finite automata and Burnside's problem for periodic groups
• The Automorphism Groups of Regular Trees
• A topology for free groups and related groups

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