Z^n中具有自由正则长函数的群
Groups with free regular length functions in Z^n
摘要：
这是第一个文件在一系列的三个，我们采取了统一理论的非阿基米德群作用，长度函数和无限的话。我们的主要目标是证明Z^n-树上的群作用是研究群的一个有力工具。所有自由作用于-树的有限生成群也自由作用于某些Z^n-树，但后者形成了一个更大的类。$Z^n-动作的所有构造的自然有效性（这不是R-树的情况）伴随着一个鲁棒的算法理论。本文描述了Z^n-树上自由正则有限生成群的代数结构，并给出了这种作用的充要条件.
英文摘要：
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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