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.

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

Finitely generated nilpotent groups are finitely presented and residually finite

Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...