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Faithful real representations of groups of $F$-type | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 9، شماره 3، آذر 2020، صفحه 143-155 اصل مقاله (220.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.112439.1494 | ||
| نویسندگان | ||
| Benjamin Fine* 1؛ Anja Moldenhauer2؛ Gerhard Rosneberger3 | ||
| 1Department of Mathematics Fairfield Universiry Fairfield, CT 06840 | ||
| 2Department of Mathematics University of Hamburg | ||
| 3Department of Mathematics University of Hmaburg | ||
| چکیده | ||
| Groups of $F$-type were introduced in [B. Fine and G. Rosenberger, Generalizing Algebraic Properties of Fuchsian Groups, \emph{London Math. Soc. Lecture Note Ser.}, \textbf{159} (1991) 124--147.] as a natural algebraic generalization of Fuchsian groups. They can be considered as the analogs of cyclically pinched one-relator groups where torsion is allowed. Using the methods In [B. Fine. M. Kreuzer and G. Rosenberger, Faithful Real Representations of Cyclically Pinched One-Relator Groups, Int. J. Group Theory, 3 (2014) 1--8.] we prove that any hyperbolic group of $F$-type has a faithful representation in $PSL(2,\mathbb R)$. From this we also obtain that a cyclically pinched one-relator group has a faithful real representation if and only if it is hyperbolic. We further survey the many nice properties of groups of $F$-type. | ||
| کلیدواژه‌ها | ||
| hyperbolic group؛ Fuchsian group؛ Group of $F$-type؛ faithful representation | ||
| مراجع | ||
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[1] M. Aab and G. Rosenberger, Subgroup separable free products with cyclic amalgamtion, Results in Math., 28 (1995) 185–194. [2] P. Ackermann, B. Fine and G. Rosenberger, On Surface Groups: Motivating Examples in Combinatorial Group Theory, London Math. Soc. Lecture Note Ser., 339 (2007) 96–129. [3] R. B. J. T. Allenby, Conjugacy Separability of a class of 1-relator products, Proc. Amer. Math. Soc., 116 (1992) 621–628. [4] R. B. J. T. Allenby and C. Y. Tang, Subgroup Separability of generalized free products of free-by-finite groups, Canad. Math. Bull., 36 (1993) 385–389. [5] G. Baumslag, B. Fine, C. Miller and D. Troeger, Virtual Properties of Cyclically Pinched One-Relator Groups, Internat. J. Algebra Comput., 19 (2009) 213–227. [6] M. Bestvina and M. Feighn, A combination theorem for negatively curved groups, J. Differential Geom., 35 (1992) 85–101. [7] F. Dahmani and V. Guiradel, The isomorphism problem for all hyperbolic groups, Geom. Funct. Anal., 21 (2011) 223–300. [8] B. Fine and G. Rosenberger, Algebraic generalizations of discrete groups, Marcel Dekker, 2000.
[9] B. Fine and G. Rosenberger, Generalizing Algebraic Properties of Fuchsian Groups, London Math. Soc. Lecture Note Ser., 159 (1991) 124–147. [10] B. Fine and G. Rosenberger, Classification of all generating pairs of two generator Fuchsian groups, London Math. Soc. Lecture Note Ser., 211 (1995) 203–232. [11] B. Fine and G. Rosenberger, The Freiheitssatz and its extensions, Contemp. Math., 169 (1994) 213–252.
[12] B. Fine and G. Rosenberger, Groups Which Admit Essentially Faithful Representations, New Zealand J. Math., 25 (1996) 1–7. [13] B. Fine, A. Gaglione, G. Rosenberger and D. Spellman, On CT and CSA Groups and Related Ideas, J. Group Theory, 19 (2016) 923–940. [14] B. Fine, A. Gaglione, A. Myasnikov, G. Rosenberger and D. Spellman, The Elementary Theory of Groups , De Gruyter, 2016. [15] B. Fine, A. Hempel and G. Rosenberger, Algebraic Extensions of Certain Discrete Groups, Analele Universitatii din Timisoara - Romanian Journal of Mathematics -Proceedings of the International Conference on Group Theory, 1993 57-91. [16] B. Fine. M. Kreuzer and G. Rosenberger, Faithful Real Representations of Cyclically Pinched One-Relator Groups, Int. J. Group Theory, 3 (2014) 1–8. [17] B. Fine, G. Rosenberger and M. Stille, Euler Characteristics of One-Relator Products of Cyclics, Comm. Algebra, 21 (1993) 4353–4359. [18] A. Juhasz and G. Rosenberger, On the combinatorial curvature of groups of F-type and other one-relator free products, Contemp. Math., 169 (1994) 373–384. [19] S. Katok, Fuchsian Groups, University of Chicago Press, 1992.
[20] O. Kharlamapovich and A. Myasnikov, Hyperbolic Groups and Free Constructions, Trans. Amer. Math. Soc., 50 (1998) 571–613. [21] G. Niblo, Fuchsian groups are strongly subgroup separable, (preprint).
[22] G. Rosenberger, The isomorphism problem for cyclically pinched one-relator groups, J. Pure Appl. Algebra, 95 (1994) 75–86. [23] Z. Sela, The Isomorphism Problem for Hyperbolic Groups I., Ann. of Math. (2), 141 (1995) 217–283. | ||
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