Discriminating Completions of Hyperbolic Groups |
| |
Authors: | Gilbert Baumslag Alexei Myasnikov Vladimir Remeslennikov |
| |
Institution: | (1) City College of New York (CUNY), New York, NY, 10031, U.S.A.;(2) Omsk University, Omsk, Russia |
| |
Abstract: | A group G is called an A-group, where A is a given Abelian group, if it comes equipped with an action of A on G which mimics the way in which Z acts on any group. This action is codified in terms of certain axioms, all but one of which were introduced some years ago by R. C. Lyndon. For every such G and A there exists an A-exponential group G
A
which is the A-completion of G. We prove here that if G is a torsion-free hyperbolic group and if A is a torsion-free Abelian group, then the Lyndon's type completion G
A
of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about G
A
. |
| |
Keywords: | hyperbolic groups completions discrimination algebraic geometry over groups |
本文献已被 SpringerLink 等数据库收录! |
|