This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.
On power- and commutation transitive, power commutative, and restricted Gromov groups by P. Ackermann, V. grosse Rebel, and G. Rosenberger Braid-based cryptography by P. Dehornoy Discriminating and squarelike groups I: Axiomatics by B. Fine, A. M. Gaglione, and D. Spellman The density of small words in a free group is 0 by R. Z. Goldstein Braid groups and Aut(F$ 2$) are not rigid by S. P. Humphries On varieties of groups in which all periodic groups are abelian by S. V. Ivanov and A. M. Storozhev Subgroups of fully residually free groups: Algorithmic problems by O. G. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov, and D. E. Serbin Weak hyperbolicity and free constructions by D. V. Osin Some properties of the conjugacy class growth function by I. Rivin Boundary test elements by E. C. Turner and C. F. Rocca Geodesics in the braid group on three strands by L. Sabalka Remarks on the growth of inverse semigroups by L. M. Shneerson Assessing security of some group based cryptosystems by V. Shpilrain.