Abstract
The authors use geometric techniques to prove that the restricted wreath product F ≀ ℂ is a quasi-isometrically embedded subgroup of Thompson’s group F.
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Belk, J. M., Thompson’s group F, PhD Thesis, Cornell University, 2004.
Burillo, J., Quasi-isometrically embedded subgroups of Thompson’s group F, J. Algebra, 212(1), 1999, 65–78.
Burillo, J. and Cleary S., Metrics and embeddings of generalizations of Thompson’s group F, Trans. Amer. Math. Soc., 353(4), 2001, 1677–1689.
Cannon, J. W., Floyd, W. J. and Parry W. R., Introductory notes on Richard Thompson’s groups, L’Enseignement Mathmatique, 42, 1996, 215–256.
Cleary, S., Distortion of wreath products in some finitely presented groups, Pacific J. Math., 228(1), 2006, 53–61.
Cleary, S. and Taback, J., Geometric quasi-isometric embeddings into Thompson’s group F, New York J. Math., 9, 2003, 141–148.
Cleary, S. and Taback, J., Combinatorial properties of Thompson’s group F, Trans. Amer. Math. Soc., 356(7), 2004, 2825–2849.
Gromov, M., Asymptotic invariants of infinite groups, Geometric Group Theory, Vol. 2, Proceedings of the Symposium Held at Sussex University, Brighton, July, 1991 (London Math. Soc. Lecture Note Ser. 182), Cambridge Univ. Press, Cambridge, 1993.
Guba, V. S. and Sapir, M. V., On subgroups of the R. Thompson group F and other diagram groups, Mat. Sb., 190(8), 1999, 3–60.
Guba, V. S. and Sapir, M. V., Diagram group, Mem. Amer. Math. Soc., 130(620), 1997, viii+117.
Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. Ser. A, 262, 1961, 455–475.
Parry, W., Growth series of some wreath products, Trans. Amer. Math. Soc., 331(2), 1992, 751–759.
Stalder, Y. and Valette, A., Wreath products with the integers, proper actions and Hilbert space compression, Geom. Dedicata, 124, 2007, 199–211.
Ol’shanskii, A. Y., On subgroup distortion in finitely presented groups, Mat. Sb., 188(11), 1997, 51–98; English transl., Sb. Math., 188, 1997, 1617–1664.
Ol’shanskii, A. Y., Distortion functions for subgroups, Geometric Group Theory Down Under (Canberra, Australia, 1996), de Gruyter, Berlin, 1999, 281–291.
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This work was supported by the National Natural Science Foundation of China (Nos. 11226122, 11301224, 11231002) and the Zhejiang Provincial Natural Science Foundation of China (No. LQ12A01015).
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Wu, Y., Chen, X. Distortion of wreath products in Thompson’s group F . Chin. Ann. Math. Ser. B 35, 801–816 (2014). https://doi.org/10.1007/s11401-014-0851-y
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DOI: https://doi.org/10.1007/s11401-014-0851-y