Groups with free regular length functions in Zⁿ

2009/07/14 by Olga Kharlampovich, Alexei Miasnikov, Kharlampovich, Olga +5 · 1 citation
Mathematics · #20 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20

paper · pdf · doi:10.48550/arxiv.0907.2356

40 pages

arxiv created 2009/07/21 · arxiv updated 2009/12/01

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 Zⁿ-trees give one a powerful tool to study groups. All finitely generated groups acting freely on -trees also act freely on some Zⁿ-trees, but the latter ones form a much larger class. The natural effectiveness of all constructions for Zⁿ-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 Zⁿ-trees and give necessary and sufficient conditions for such actions.

Cited by

• Actions, length functions, and non-archemedian words

Related

• Regular completions of ℤⁿ-free groups
• Limit groups and groups acting freely on \bbRⁿ-trees
• Length Function Compatibility for Group Actions on Real Trees
• Groups acting freely on Λ-trees
• Translation length formula for two-generated groups acting on trees