TRANSVERSALS AS GENERATING SETS IN FINITELY GENERATED GROUPS

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.

Automorphisms of Free Groups Have Finitely Generated Fixed Point Sets

An automorphism of a finitely generated free group F extends to a homeomorphism of the end completion E of F. The set of fixed points of this homeomorphism is finitely generated in a certain sense. In particular this implies that the subgroup of elements fixed by the automorphism is finitely generated in the usual sense. The emphasis on E instead of F in this paper is analogous to Thurston’s st...

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...

Combinatorics of Finitely Generated Groups

of the Dissertation Combinatorics of Finitely Generated Groups