TY - JOUR
ID - 23755
TI - Faithful real representations of groups of $F$-type
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Fine, Benjamin
AU - Moldenhauer, Anja
AU - Rosneberger, Gerhard
AD - Department of Mathematics
Fairfield Universiry
Fairfield, CT 06840
AD - Department of Mathematics
University of Hamburg
AD - Department of Mathematics
University of Hmaburg
Y1 - 2020
PY - 2020
VL - 9
IS - 3
SP - 143
EP - 155
KW - hyperbolic group
KW - Fuchsian group
KW - Group of $F$-type
KW - faithful representation
DO - 10.22108/ijgt.2018.112439.1494
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_23755.html
L1 - https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdf
ER -