Tarski's problem about the elementary theory of free groups has a positive solution.
Test elements and test rank of a free metabelian group.
The classification of groups in which every product of four elements can be reordered
The Conjugacy Problem for Free Products of Sixth-Groups with Cyclic Amalgamation.
The conjugacy problem for groups, and Higman embeddings.
The conjugacy problem for relatively hyperbolic groups.
The equation in partially commutative groups.
The equation in partially commutative groups.
The genus problem for one-relator products of locally indicable groups.
The Grushko decomposition of a finite graph of finite rank free groups: an algorithm.
The isomorphism problem for toral relatively hyperbolic groups
We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorphism problem for finite volume hyperbolic -manifolds, for . In the course of the proof of the main result,...
The Malnormality of Certain Subgroups of Small Cancellation Groups.
The Symmetries of Classes of Elements in a Free Group of Rank Two.
The virtual and universal braids
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi-direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi-direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as quotients the singular braid group, virtual...
The width of a power of a free nilpotent group of nilpotency class 2.
The word problem in polycyclic groups is elementary
Two decidable Markov properties over a class of solvable groups.
Type-dependent positive definite functions on free products of groups