FULLY RESIDUALLY FREE GROUPS AND GRAPHS LABELED BY INFINITE WORDS

Autor:	Vladimir N. Remeslennikov, Alexei Myasnikov, Denis Serbin
Rok vydání:	2006
Předmět:	Combinatorics Ring (mathematics) Limit (category theory) Stallings theorem about ends of groups Integer Group (mathematics) General Mathematics Free group Basis (universal algebra) Characterization (mathematics) Mathematics
Zdroj:	International Journal of Algebra and Computation. 16:689-737
ISSN:	1793-6500 0218-1967
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e31797f46cf7e4aefba94c8f68188812 https://doi.org/10.1142/s0218196706003141 Zobrazit plný text záznamu