A graph product is the fundamental group of a graph of groups Amongst the simplest examples are HNN groups and free products with amalgamation. The conjugacy problem is solvable for recursively presented graph products with cyclic edge groups over finite graphs if the vertex groups have solvable conjugacy problem and the sets of cyclic generators in them are semicritical. For graph products ove...

We prove that the Schützenberger graph of any element of the HNN-extension of a finite inverse semigroup S with respect to its standard presentation is a context-free graph in the sense of [11], showing that the language L recognized by this automaton is context-free. Finally we explicitly construct the grammar generating L, and from this fact we show that the word problem for an HNN-extension ...

Abstract In this paper we introduce the notion of existentially closed Leibniz algebras. Then use HNN-extensions algebras in order to prove an embedding theorem.

Abstract Recently, I. J. Leary and A. Minasyan [Commensurating HNN extensions: Nonpositive curvature biautomaticity, Geom. Topol. 25 (2021), 4, 1819–1860] studied the class of groups G ⁢ ( A , L stretchy="false">) </m:math...

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...

Abstract The authors are studying hardware neural networks (HNN) to control the locomotion of microrobot. chip is integrated circuit HNN. We proposed electrostatic motor that new actuator microrobot in our previous research. used waveform generator generate driving waveform. In this paper, will propose using chip. cell body model basic component outputs 3 MHz frequency electrical oscillated pul...

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.

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we have a group with infinitely many ends has infinite dimensional second bounded cohomology.