Infinite words and universal free actions

Olga Kharlampovich; Alexei Myasnikov; Denis Serbin

doi:10.1515/gcc-2014-0005

Published by De Gruyter April 11, 2014

Infinite words and universal free actions

Olga Kharlampovich , Alexei Myasnikov and Denis Serbin

From the journal Groups Complexity Cryptology

https://doi.org/10.1515/gcc-2014-0005

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Abstract.

This is the second paper in a series of four, where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Here, for an arbitrary group G of infinite words over an ordered abelian group Λ we construct a Λ-tree ΓG equipped with a free action of G. Moreover, we show that ΓG is a universal tree for G in the sense that it isometrically and equivariantly embeds into every Λ-tree equipped with a free G-action compatible with the original length function on G. Also, for a group G acting freely on a Λ-tree Γ we show how one can easily obtain an embedding of G into the set of reduced infinite words R(Λ,X), where the alphabet X is obtained from the action G on Γ.

Keywords: Infinite words; group actions on trees; Λ-trees

MSC: 20F65; 20E08

Received: 2014-2-5

Published Online: 2014-4-11

Published in Print: 2014-5-1

Infinite words and universal free actions

Abstract.

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