## Regular trees and their automorphisms |

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### Common terms and phrases

1-rooted tree 3-group Q automata Automaton automor automorphism group base group binary tree Burnside groups congruence subgroups conjugacy classes conjugate connecting set constructed copies coset tree define denote direct product dyadic integers elements embedded enumerable epimorphism esgotada faithful representation finite p-group finite state automorphisms finitely generated periodic finitely presentable fixes free group Functionally recursive automorphisms GL(n Golod groups Grigorchuk group algebra group G group G(Y group of automorphisms group of finite group of tree Gupta-Sidki homomorphism induces infinite number infinite order infinite products infinitely iterated isomorphic iterated structure k-th level Let G Let H level vertices linear group locally finite maximal 2-subgroup natural number nontrivial normal subgroup obtain p-adic tree periodic group permutation phisms Pi(Y pointwise prime number Problem proper quotient Proposition recursive set REGULAR TREES Residually finite groups sequence set of automorphisms subgroups of tree subnormal subgroups subtree headed Suppose TEORIA Theorem tree automorphisms wreath product