Unsolved Problems in Group Theory. The Kourovka Notebook

This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965. This is the 19th edition, which contains 111 new problems and a number of comments on about 1000 problems from the previous editions.Comment: A few new solutions and references have been added or update

Topics in hyperbolic groups

Hyperbolic groups are a class of groups introduced by Gromov in 1987, which form an important part of geometric group theory. In Chapter 1, we give an introduction to this subject. In Chapter 2, we use the theory of complexes of groups to show that the integral homology and cohomology groups of a hyperbolic group are computable by a Turing machine. In Chapter 3, we present the boundary of a hyperbolic group as an inverse limit of topological spaces and use this to give computable estimates for properties of the boundary. In Chapter 4, we investigate symbolic dynamic properties concerning hyperbolic groups. In paricular, we give symbolic codings for the actions on the boundary of a hyperbolic and actions on the geodesic flow on a hyperbolic group. In Chapter 5 we investigate the problem of determining when graphs are Cayley graphs. The graphs which we are concerned with are regular and semi-regular planar graphs

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th