TY - JOUR
T1 - Discriminating completions of hyperbolic groups
AU - Baumslag, Gilbert
AU - Myasnikov, Alexei
AU - Remeslennikov, Vladimir
PY - 2002
Y1 - 2002
N2 - 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 GA 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 GA of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about GA.
AB - 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 GA 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 GA of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about GA.
KW - Algebraic geometry over groups
KW - Completions
KW - Discrimination
KW - Hyperbolic groups
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U2 - 10.1023/A:1019687202544
DO - 10.1023/A:1019687202544
M3 - Article
AN - SCOPUS:0036344629
SN - 0046-5755
VL - 92
SP - 115
EP - 143
JO - Geometriae Dedicata
JF - Geometriae Dedicata
IS - 1
ER -