The group of all finite-state automorphisms of a regular rooted tree has a minimal generating set.

DOI10.1007/s10711-016-0145-5zbMath1347.20029OpenAlexW2286993093MaRDI QIDQ303986

Yaroslav Lavrenyuk

Publication date: 23 August 2016

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-016-0145-5

zbMATH Keywords

minimal generating setsautomorphisms of rooted treesfinite-state automorphismspermutational wreath products

Mathematics Subject Classification ID

Trees (05C05) Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Automorphisms of infinite groups (20E36) Extensions, wreath products, and other compositions of groups (20E22) Groups acting on trees (20E08)

Related Items (1)

Minimal generating sets in groups of $p$-automata

Cites Work

• Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function.
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• Finite state wreath powers of transformation semigroups.
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• Probabilistic Generation of Wreath Products of Non-abelian Finite Simple Groups
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