On finite state automaton actions of HNN extensions of free abelian groups

Keywords: automaton group, automorphism of rooted tree, HNN extension
Published online: 2021-06-28

Abstract


HNN extensions of free abelian groups are considered. For arbitrary prime $p$ it is introduced a class of such extensions that act by finite automaton permutations over an alphabet $ \mathsf{X} $ of cardinality $p$ and belong to $p$-Sylow subgroup of the group of automaton permutations over such $ \mathsf{X} $. As a corollary it implies that all corresponding HNN extensions are residually $p$-finite.

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How to Cite
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Prokhorchuk V. On Finite State Automaton Actions of HNN Extensions of Free Abelian Groups. Carpathian Math. Publ. 2021, 13 (1), 180-188.