Fully Residually Free Groups and Graphs Labeled by Infinite Words
نویسندگان
چکیده
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.
منابع مشابه
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عنوان ژورنال:
- IJAC
دوره 16 شماره
صفحات -
تاریخ انتشار 2006