Geodesic
A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup
Jan Kim1 orcid ; Donghi Lee1 orcid
1Pusan National University, Busan, South Korea
Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1275-1289

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DOI

We produce an example demonstrating that every finitely generated relatively hyperbolic group with respect to a collection of Hopfian subgroups need not be Hopfian. This answers a question of Osin (2006) in the negative.
DOI : 10.4171/ggd/782
Classification : 20F65, 20F06
Mots-clés : non-Hopfian group, relatively hyperbolic group, peripheral subgroup

Jan Kim  1   ; Donghi Lee  1

1 Pusan National University, Busan, South Korea 
Jan Kim; Donghi Lee. A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup. Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1275-1289. doi: 10.4171/ggd/782
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     author = {Jan Kim and Donghi Lee},
     title = {A {non-Hopfian} relatively hyperbolic group with respect {to~a~Hopfian} subgroup},
     journal = {Groups, geometry, and dynamics},
     pages = {1275--1289},
     year = {2024},
     volume = {18},
     number = {4},
     doi = {10.4171/ggd/782},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/782/}
}
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