Bounded HNN presentations

The bounded and precise word problems for presentations of groups

We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE. The main technical result of the paper states that, for certain finit...

Perfect 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...

Subgroups of Quasi-hnn Groups

Hnn Extensions of Von Neumann Algebras

Reduced HNN extensions of von Neumann algebras (as well as C-algebras) will be introduced, and their modular theory, factoriality and ultraproducts will be discussed. In several concrete settings, it will be illustrated how our results can be applied.

Theories 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...