Groups with free regular length functions in Z n

Olga Kharlampovich, Alexei Myasnikov, Vladimir Remeslennikov, Denis Serbin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This is the first paper in a series of three where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Our main goal is to show that group actions on Z n-trees give one a powerful tool to study groups. All finitely generated groups acting freely on R-trees also act freely on some Z n-trees, but the latter ones form a much larger class. The natural effectiveness of all constructions for Z n-actions (which is not the case for R-trees) comes along with a robust algorithmic theory. In this paper we describe the algebraic structure of finitely generated groups acting freely and regularly on Z n-trees and give necessary and sufficient conditions for such actions.

Original languageEnglish
Pages (from-to)2847-2882
Number of pages36
JournalTransactions of the American Mathematical Society
Volume364
Issue number6
DOIs
StatePublished - 2012

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