The paper by O. Bogopolski and A. Vikentiev describes some particularly useful?niteindexsubgroupsoftheautomorphismgroupofa?nitelygeneratedfree group. One of their uses may be to attack the problem on the Kazhdan property (T) for these groups. The paper of A. Juhasz contains a solution of the di?cult membership problem in a subclass of one-relator groups. Papers of F. Matucci, D. Savchuk and R. Zarzycki will attract the attention of those who want to know more about groups of transformations of the unit interval [0,1], in particular about the famous Thompson s group F and its limit properties. The paper by A.J. Duncan, V. Dieckert and A.G. Myasnikov contains a very thoroughsurveyonrewritingsystemswithnewissuesonin?niterewritingsystems. The paper by L. Frenkel, A.G. Myasnikov and V.N. Remeslennikov is devoted to theproblemofhowto measuresomesubsets infreegroupsbyusingrandomwalks. The results of this paper may be used for designing algorithms that run fast on almost all inputs. This paper as well as the paper by M. Hock and B. Tsaban are highly recommended to specialists in cryptography. Finally, the paper by D. Goncalves and P. Wong is devoted to the twisted conjugacy in 2-dimensional crystallographic groups. We are very grateful to the organizations that supported these two conferences: TheconferenceinDortmundwasorganizedbyO.Bogopolski,M.-T.Bochnig, G.Rosenberger,V.Shpilrainand E.Ventura.Thisconferencewas?nancially supported by DAAD (Deutscher Akademischer Austauschdienst), by DFG (Deutsche Forschungsgemeinschaft), and by the Universit at Dortmund. The URL address for its homepage is http://www.mathematik.uni-dortmund.de/?gcgta/.

Interesting articles about a very modern and active field of mathematics Representation of different aspects of modern geometrical and combinatorial group theory: from group actions on spaces to algorithmic problems passing through cryptography applications Includes supplementary material: sn.pub/extras

Inhalt
Subgroups of Small Index in Aut(F n ) and Kazhdan's Property (T).- Dynamics of Free Group Automorphisms.- Geodesic Rewriting Systems and Pregroups.- Regular Sets and Counting in Free Groups.- Twisted Conjugacy for Virtually Cyclic Groups and Crystallographic Groups.- Solving Random Equations in Garside Groups Using Length Functions.- An Application of Word Combinatorics to Decision Problems in Group Theory.- Equations and Fully Residually Free Groups.- The F N -action on the Product of the Two Limit Trees for an Iwip Automorphism.- Mather Invariants in Groups of Piecewise-linear Homeomorphisms.- Algebraic Geometry over the Additive Monoid of Natural Numbers: Systems of Coefficient Free Equations.- Some Graphs Related to Thompson's Group F.- Generating Tuples of Virtually Free Groups.- Limits of Thompson's Group F.