Finitely generated non-Hopfian 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 Presentable, Non-hopfian Groups with Kazhdan’s Property and Infinite Outer Automorphism Group

We give simple examples of finitely presented Kazhdan groups with infinite outer automorphism groups, as arithmetic lattices in Lie groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. We also use results of Abels about compact presentability of p-adic groups to exhibit a finitely presented non-Hopfian Kazhdan group. This answer...