Page Introduction 269 Notation and terminology 271 I. Basic facts 271 1. Review of IM 271 2. Review of AM 273 3. Solvable groups, aG, finite Priifer rank, FP 2 , and HNN-extensions . 276 4. Matrix computation of AM in the finite rank case . . . . 277 5. Finiteness conditions: F P m and finite presentation . . . . 278 6. The properties m-tameness and w-domestication 280 II. Proof that Hm{G, Y\ R...

We prove here that a finitely presented group with a free quotient of rank n is an HNN-extension with n stable letters of a finitely generated group where the associated subgroups are finitely generated. This theorem has a number of consequences. In particular, in the event that the free quotient is cyclic it reduces to an elementary and quick proof of a theorem of Bieri and Strebel. 1. Finitel...

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 torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order proble...

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...

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 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.

Although neural networks have been widely applied to medical problems in recent years, their applicability has been limited for a variety of reasons. One of these barriers has been the inability to discriminate rare classes of solutions (i.e., the identification of categories that are infrequent). In this article, I demonstrate that a system of hierarchical neural networks (HNN) can overcome th...