Homotopy Classification of Lens Spaces for One-relator Groups with Torsion

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 up to homotopy type. We also discuss the noncancellation aspect of these Lens spaces.