Representation of tree permutations by words

Author:
John A. Maroli

Journal:
Proc. Amer. Math. Soc. **110** (1990), 859-869

MSC:
Primary 06A06; Secondary 06F15, 20B27

DOI:
https://doi.org/10.1090/S0002-9939-1990-1037214-X

MathSciNet review:
1037214

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Abstract | References | Similar Articles | Additional Information

Abstract: The problem of solving equations in groups can be stated as follows: given a group and a free group , for which pairs with , is it possible to find elements such that ? We investigate the corresponding question of solving equations in the group of all automorphisms of a transitive tree . If the tree has isomorphic cones at a branch point, then certain equations of the form cannot be solved (Theorem 2.3). If the tree is sufficiently transitive, we find large classes of equations which can be solved (Theorems 2.13, 2.16).

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1037214-X

Article copyright:
© Copyright 1990
American Mathematical Society