The -local subgroups of the groups with a generalized finite element of order 2 or 4.
The Fibonacci automorphism of free Burnside groups
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
The Fibonacci automorphism of free Burnside groups
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups.
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
The fixed group of an automorphism of a word hyperbolic group is rational.
The Frattini Subgroup of Locally Free Groups.
The Functional Equation. (Short Communication).
The fundamental groups of subsets of closed surfaces inject into their first shape groups.
The genus problem for one-relator products of locally indicable groups.
The geometric invariants of direct products of virtually free groups.
The geometry of abstract groups and their splittings.
A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL2 and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD2 groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PDn groups. Notions of quasi-isometry,...
The groupoid of varieties of idempotent semigroups.
The Grushko decomposition of a finite graph of finite rank free groups: an algorithm.
The holomorphic automorphism group of the complex disk.
The homology of Peiffer products of groups.
The homomorphic images of infinite symmetric groups.
The irreducible six-dimensional complex representations of that are nontrivial on .
The Isomorphism Problem for One-relator Groups with Non-trivial Centre.
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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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,...