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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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[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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