Faithful real representations of groups of $F$-type
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 anal...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2020-09-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdf |
| _version_ | 1818487546891468800 |
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| author | Benjamin Fine Anja Moldenhauer Gerhard Rosneberger |
| author_facet | Benjamin Fine Anja Moldenhauer Gerhard Rosneberger |
| author_sort | Benjamin Fine |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T16:39:21Z |
| format | Article |
| id | doaj.art-c84e31721dec4feaa50ddfb19ebdb1ea |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-10T16:39:21Z |
| publishDate | 2020-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-c84e31721dec4feaa50ddfb19ebdb1ea2022-12-22T01:41:16ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692020-09-019314315510.22108/ijgt.2018.112439.149423755Faithful real representations of groups of $F$-typeBenjamin Fine0Anja Moldenhauer1Gerhard Rosneberger2Department of Mathematics Fairfield Universiry Fairfield, CT 06840Department of Mathematics University of HamburgDepartment of Mathematics University of HmaburgGroups 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. https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdfhyperbolic groupfuchsian groupgroup of $f$-typefaithful representation |
| spellingShingle | Benjamin Fine Anja Moldenhauer Gerhard Rosneberger Faithful real representations of groups of $F$-type International Journal of Group Theory hyperbolic group fuchsian group group of $f$-type faithful representation |
| title | Faithful real representations of groups of $F$-type |
| title_full | Faithful real representations of groups of $F$-type |
| title_fullStr | Faithful real representations of groups of $F$-type |
| title_full_unstemmed | Faithful real representations of groups of $F$-type |
| title_short | Faithful real representations of groups of $F$-type |
| title_sort | faithful real representations of groups of f type |
| topic | hyperbolic group fuchsian group group of $f$-type faithful representation |
| url | https://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdf |
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