In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) = G and whose universal cover K̃ has the proper homotopy type of a 3-manifold (with boundary).

We prove that for an action of a finite group G on a systolic complex X there exists a G–invariant subcomplex of X of diameter 5. For 7–systolic locally finite complexes we prove there is a fixed point for the action of any finite G. This implies that free products with amalgamation (and HNN extensions) of 7–systolic groups over finite subgroups are also 7–systolic.

— Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A...

A general framework for hybrids of hidden Markov models (HMMs) and neural networks (NNs) called hidden neural networks (HNNs) is described. The article begins by reviewing standard HMMs and estimation by conditional maximum likelihood, which is used by the HNN. In the HNN, the usual HMM probability parameters are replaced by the outputs of state-specific neural networks. As opposed to many othe...

A countable discrete group G is called W?-superrigid (resp. C?-superrigid) if it completely recognizable from its von Neumann algebra L(G) reduced C?-algebra Cr?(G)). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several classes of groups which appear as direct products, semidirect products with non-amenable core and iterations amalgamated free HNN-extensio...

We show that the finitely presented groups with unsolvable word problem given by the Boone-Britton construction have cohomological dimension 2. More precisely we show these groups can be obtained from a free group by successively forming HNN-extensions where the associated subgroups are finitely generated free groups. Also the presentations obtained for these groups are aspherical. Using this w...

In his recent series of lectures, Prof. B. I. Plotkin discussed geometrical properties of the variety of associative K-algebras. In particular, he studied geometrically noetherian and logically noetherian algebras and, in this connection, he asked whether there exist uncountably many simple K-algebras with a fixed finite number of generators. We answer this question in the affirmative using bot...

Quasi-HNN groups can be characterized as a generalization of HNN groups. In this paper, we show that if G * is a quasi-HNN group of base G, then either any two conjugates of G are identical or their intersection is contained in a conjugate of an associated subgroup of G.