FULLY RESIDUALLY FREE GROUPS AND GRAPHS LABELED BY INFINITE WORDS
2006 ◽
Vol 16
(04)
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pp. 689-737
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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.
2006 ◽
Vol 16
(06)
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pp. 1031-1045
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1971 ◽
Vol 5
(1)
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pp. 87-94
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2012 ◽
Vol 22
(04)
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pp. 1250030
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1999 ◽
Vol 09
(06)
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pp. 687-692
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2012 ◽
Vol 22
(02)
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pp. 1250008
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2002 ◽
Vol 132
(1)
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pp. 117-130
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2010 ◽
Vol 20
(03)
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pp. 343-355
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