Hopficity of certain HNN-extensions

Subgroup Separability of HNN-Extensions with Abelian Base Group

“…A similar characterisation was given by Wong [22] for a special case. In fact, Wong, using the results in [3], gives a characterisation for subgroup separability of HNN-extensions where the associated subgroups have finite index as subgroups of the base group.…”

Representationes no Abelianas de los Grupos de Baumslag-Solitar

“…However, we can get one from mathoverflow. From the results displayed in this paper and some restrictions given in [7] and [1] about the residually finiteness of the Baumslag-Solitar groups, we prove that BS(n, m) only admits a faithful representation into SL(2, C) when n = 1 and |m| > 1. This result overlaps with what was mentioned in the previous paragraph, but we propose a different method that might be of interest for those working in Kleinian and Fuchsian groups.…”

Commensurating HNN-extensions: non-positive curvature and biautomaticity

“…Since |b| A ≤ 2κ + 1 for any b ∈ B, by (2), and p has the same endpoints as p, q has the same endpoints as q, we see that d A (p − , q − ) ≤ 2κ + 1 and d A (p + , q + ) ≤ 2κ + 1. Therefore the paths p and q ζ-fellow travel in Γ(G, A), where ζ := ε(2κ + 1).…”

“…Then: We want an analogous statement to (4) above, but for isometries that lie in the commensurator of L rather than in its normalizer. For this it is easier first to describe a different statement that is equivalent to (3).…”