Homogeneous bands

A band B is a semigroup such that e2=e for all e∈B. A countable band is called homogeneous if every isomorphism between finitely generated subbands extends to an automorphism of the band. 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.