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arXiv · 0907.2356

Groups with free regular length functions in Z^n

Olga Kharlampovich·Alexei Miasnikov·Vladimir Remeslennikov·Denis Serbin
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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 -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.

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Olga Kharlampovich, Alexei Miasnikov, Vladimir Remeslennikov, Denis Serbin. 2009-07-21. Groups with free regular length functions in Z^n. https://arxiv.org/abs/0907.2356

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