Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups | Zendy

Luc Guyot | Zendy; Yves Stalder | Zendy

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Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups

Author(s) -

Luc Guyot,

Yves Stalder

Publication year - 2012

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/165

Subject(s) - mathematics , dimension (graph theory) , space (punctuation) , finitely generated abelian group , pure mathematics , group (periodic table) , combinatorics , computer science , chemistry , organic chemistry , operating system

We prove that the limits of Baumslag-Solitar groups which we previously studied are non-linear hopfian C*-simple groups with infinitely many twisted conjugacy classes. We exhibit infinite presentations for these groups, classify them up to group isomorphism, describe their automorphisms and discuss the word and conjugacy problems. Finally, we prove that the set of these groups has non-zero Hausforff dimension in the space of marked groups on two generators.

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