Commensurated subgroups in finitely generated branch groups

Commensurated Subgroups and Ends of Groups

If G is a group, then subgroups A and B are commensurable if A ∩B has finite index in both A and B. The commensurator of A in G, denoted CommG(A), is {g ∈ G|(gAg−1) ∩A has finite index in both A and gAg−1}. It is straightforward to check that CommG(A) is a subgroup of G. A subgroup A is commensurated in G if CommG(A) = G. The centralizer of A in G is a subgroup of the normalizer of A in G which...

On Intersections of Finitely Generated Subgroups of Free Groups

and asked if the factor 2 can be dropped. If one translates her approach (which is a slight modification of Howson's) to graph-theoretic terms, it easily shows that the answer is often "yes"in fact, for most U the answer is "yes" for all V. According to Gersten [G], the above problem has come to be known as the "Haana Neumann Conjecture." Using ideas of immersions of graphs originating from Sta...

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...