A construction is given, in a variety of groups, of a ``functorial center'' called the endocenter. The endocenter facilitates the identification of universal multiplication groups of groups in the variety, addressing the problem of determining when combinatorial multiplication groups are universal.
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
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,...