TY - JOUR
T1 - Groups with free regular length functions in Z n
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
AU - Remeslennikov, Vladimir
AU - Serbin, Denis
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84857660381&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84857660381&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2012-05376-1
DO - 10.1090/S0002-9947-2012-05376-1
M3 - Article
AN - SCOPUS:84857660381
SN - 0002-9947
VL - 364
SP - 2847
EP - 2882
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -