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FULLY RESIDUALLY FREE GROUPS AND GRAPHS LABELED BY INFINITE WORDS.
- Source :
-
International Journal of Algebra & Computation . Aug2006, Vol. 16 Issue 4, p689-737. 49p. 5 Diagrams, 5 Graphs. - Publication Year :
- 2006
-
Abstract
- Let F = F(X) be a free group with basis X and ℤ[t] be a ring of polynomials with integer coefficients in t. In this paper we develop a theory of (ℤ[t],X)-graphs — a powerful tool in studying finitely generated fully residually free (limit) groups. This theory is based on the Kharlampovich–Myasnikov characterization of finitely generated fully residually free groups as subgroups of the Lyndon's group Fℤ[t], the author's representation of elements of Fℤ[t] by infinite (ℤ[t],X)-words, and Stallings folding method for subgroups of free groups. As an application, we solve the membership problem for finitely generated subgroups of Fℤ[t], as well as for finitely generated fully residually free groups. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FREE groups
*GROUP theory
*GRAPHIC methods
*POLYNOMIALS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 16
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 22271817
- Full Text :
- https://doi.org/10.1142/S0218196706003141