Homogeneous Bands
  A countable band $B$ is called homogeneous if every isomorphism between finitely generated subbands extends to an automorphism of $B$. In this paper we give a complete classification of all the homogeneous bands. We prove that a homogeneous band belongs to the variety of regular bands, and has a homogeneous structure semilattice. 
Thomas Quinn-Gregson
math.RA