Intersection of finitely generated surface groups

The limit set intersection theorem for finitely generated Kleinian groups

The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Sectio...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

Combinatorics of Finitely Generated Groups

of the Dissertation Combinatorics of Finitely Generated Groups

Powers in Finitely Generated Groups

In this paper we study the set Γn of nth-powers in certain finitely generated groups Γ. We show that, if Γ is soluble or linear, and Γn contains a finite index subgroup, then Γ is nilpotent-by-finite. We also show that, if Γ is linear and Γn has finite index (i.e. Γ may be covered by finitely many translations of Γn), then Γ is soluble-by-finite. The proof applies invariant measures on amenable...