Linear and projective boundaries in HNN-extensions and distortion phenomena
نویسندگان
چکیده
منابع مشابه
Linear and projective boundaries in HNN-extensions and distortion phenomena
Linear and projective boundaries of Cayley graphs were introduced in [6] as quasi-isometry invariant boundaries of finitely generated groups. They consist of forward orbits g D 1g W i 2 No, or orbits g D 1g W i 2 Zo, respectively, of non-torsion elements g of the group G, where ‘sufficiently close’ (forward) orbits become identified, together with a metric bounded by 1. We show that for all fin...
متن کاملNon-linear ascending HNN extensions of free groups
is called an ascending HNN extension of G (or the mapping torus of the endomorphism φ). In particular, the ascending HNN extensions of free groups of finite rank are simply the groups given by presentations 〈x1, ..., xn, t | txit−1 = wi, i = 1, ..., n〉, where w1, ..., wn are words generating a free subgroup of rank n. In [BS], Borisov and Sapir proved that all ascending HNN extensions of linear...
متن کاملTheories of HNN-Extensions and Amalgamated Products
It is shown that the existential theory of G with rational constraints, over an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 is decidable, provided that the same problem is decidable in the base group H and that A is a finite group. The positive theory of G is decidable, provided that the existential positive theory of G is decidable and that A and φ(A) are proper subgroups of the base group H w...
متن کاملPerfect Subgroups of Hnn Extensions
This note includes supporting material for Guilbault’s one-hour talk summarized elsewhere in these proceedings. We supply the group theory necessary to argue that Guilbault’s tame ends cannot be pseudocollared. In particular, we show that certain groups (the interated Baumslag-Solitar groups) cannot have any non-trivial perfect subgroups. The absence of non-trivial perfect subgroups, in turn, e...
متن کاملRational Subsets in HNN-Extensions and Amalgamated Products
of a group H, where A and B are isomorphic subgroups of H and φ : A → B is an isomorphism, results from adding to H a new generator t such that the conjugation of the subgroup A ≤ H by t realizes the isomorphism φ. We also say that A and B in (2) are the associated subgroups. One of the first important applications of HNN-extensions was a more transparent proof of the celebrated result of Novik...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2015
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgth-2015-0002