%0 Journal Article
%T Faithful real representations of groups of $F$-type
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Fine, Benjamin
%A Moldenhauer, Anja
%A Rosneberger, Gerhard
%D 2020
%\ 09/01/2020
%V 9
%N 3
%P 143-155
%! Faithful real representations of groups of $F$-type
%K hyperbolic group
%K Fuchsian group
%K Group of $F$-type
%K faithful representation
%R 10.22108/ijgt.2018.112439.1494
%X 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.
%U https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdf