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.

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...

We obtain an upper bound for relative Dehn functions of amalgamated products and HNN–extensions with respect to certain collections of subgroups. Our main results generalize the combination theorems for relatively hyperbolic groups proved by Dahmani.

In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.

An explicit embedding mentioned in this problem is possible and, moreover, the finitely generated group G can in fact be two-generator. This, of course, stresses the similarity of the constructed embedding with the embedding of [4] because the latter, too, is an embedding into a two-generator group. In the current paper, we suggest two mechanisms to build the embedding mentioned. The first argu...

Garside groups are a natural lattice-theoretic generalisation of the braid and spherical type Artin–Tits groups. Here we show that class is closed under some free products with cyclic amalgamated subgroups. We deduce every tree product infinite group. Moreover, study those HNN extensions as well. Using theorem Pietrowski, conclude this paper by stating non-cyclic one-relator group if only its c...