Exponential groups 2: Extensions of centralizers and tensor completion of CSA groups

Alexey Myasnikov; Vladimir Remeslennikov

paper

Exponential groups 2: Extensions of centralizers and tensor completion of CSA groups

arXiv:math/9507203

Abstract

For a CSA group $G$ and a wide class of abelian groups $A$ we give an explicit construction for the tensor $A$ -completion of $G$ using free products with amalgamations. We apply the obtained results to the study of basic properties of $A$ -free groups. In particular, canonical and reduced forms of elements in $A$ -free groups are introduced, and then commuting and conjugate elements are described.

LaTex, 33 pages, no figures. Submitted to Intern. J. Alg. Comp