Geometriae Dedicata

, Volume 108, Issue 1, pp 193–204 | Cite as

Finite Automata of Polynomial Growth do Not Generate A Free Group

  • Said Sidki
Article

Abstract

A free subgroup of rank 2 of the automorphism group of a regular rooted tree of finite degree cannot be generated by finite-state automorphisms having polynomial growth. This result is in fact proven for rooted trees of infinite degree under some natural additional conditions.

rooted tree automorphisms of trees finite automata polynomial growth free groups 
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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Said Sidki
    • 1
  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasília DFBrazil

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