This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory.

Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory.

The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Readership

Graduate students and research mathematicians interested in combinatorial and geometric group theory.

Table of Contents

• G. Baumslag, A. G. Myasnikov, and V. Shpilrain -- Open problems in combinatorial group theory. Second edition
• I. Kapovich and N. Benakli -- Boundaries of hyperbolic groups
• P. Dehornoy -- Thin groups of fractions
• A. M. Gaglione, D. Spellman, and B. Fine -- Every abelian group universally equivalent to a discriminating group is elementarily equivalent to a discriminating group
• S. V. Ivanov -- Weakly finitely presented infinite periodic groups
• B. Khan -- Positively generated subgroups of free groups and the Hanna Neumann conjecture
• A. R. Magid -- On the proalgebraic completion of a finitely generated group
• A. D. Myasnikov, A. G. Myasnikov, and V. Shpilrain -- On the Andrews-Curtis equivalence
• C. F. Rocca, Jr. and E. C. Turner -- Test ranks of finitely generated abelian groups
• G. Rosenberger and M. Scheer -- Classification of the finite generalized tetrahedron groups
• E. Ventura -- Fixed subgroups in free groups: A survey
• A. Weaver -- Automorphisms of surfaces