Isomorphism theorems for classes of cyclically presented groups

We consider two multi-parameter classes of cyclically presented groups, introduced by Cavicchioli, Repovs and Spaggiari, that contain many previously considered families of cyclically presented groups of interest both for their algebraic and for their topological properties. Building on results of Bardakov and Vesnin, O'Brien and the previously named authors, we prove theorems that establish isomorphisms of groups within these families.