Let Ξ be a one-relator group with presentation & — ($i, •" ,%n R ) where R is not a proper power and p ^ 2. Then given any integer q, relatively prime to p, we can construct the Lens space ^(pf q) for Ξ from the cellular model C(&) of the presentation & by attaching a 3-cell via the attaching map R — 1, which generates the ideal ZΞ(R — 1) « τr2(C(^)). In this paper we classify these Lens spaces...

We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts “like an automorphism” on one particular orbit), is itself an automorphism. Then, we consider elements of a different nature, defined by means of homological prope...

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free...