@article {
author = {Fine, Benjamin and Moldenhauer, Anja and Rosneberger, Gerhard},
title = {Faithful real representations of groups of $F$-type},
journal = {International Journal of Group Theory},
volume = {9},
number = {3},
pages = {143-155},
year = {2020},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2018.112439.1494},
abstract = {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. },
keywords = {hyperbolic group,Fuchsian group,Group of $F$-type,faithful representation},
url = {https://ijgt.ui.ac.ir/article_23755.html},
eprint = {https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdf}
}