The pure cactus group is residually nilpotent

The isomorphism problem for residually torsion-free nilpotent groups

Both the conjugacy and isomorphism problems for finitely generated nilpotent groups are recursively solvable. In some recent work, the first author, with a tiny modification of work in the second author’s thesis, proved that the conjugacy problem for finitely presented, residually torsion-free nilpotent groups is recursively unsolvable. Here we complete the algorithmic picture by proving that t...

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...

Free Two-step Nilpotent Groups Whose Automorphism Group Is Complete

Dyer and Formanek (1976) proved that if N is a free nilpotent group of class two and of rank 6= 1, 3, then the automorphism group Aut(N) of N is complete. The main result of this paper states that the automorphism group of an infinitely generated free nilpotent group of class two is also complete.

The Complement of a D-Tree is Pure Shellable

An Endomorphism of a Finitely Generated Residually Finite Group

Let φ : G→ G be an endomorphism of a finitely generated residually finite group. R. Hirshon asked if there exists n such that the restriction of φ to φn(G) is injective. We give an example to show that this is not always the case.