Olga Kharlampovich – författare

This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory.

The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory.

The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

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/.