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Groups with free regular length functions in Z^n by Kharlampovich, Olga; Miasnikov, Alexei; Remeslennikov, Vladimir; Serbin, Denis is a scholarly article available to read on EtoBox.

What is Groups with free regular length functions in Z^n about?

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.

Author

Kharlampovich, Olga; Miasnikov, Alexei; Remeslennikov, Vladimir; Serbin, Denis

Published

2009

Language

EN