A natural characterization of semilattices of rectangular bands and groups of exponent 2

In a recent paper, R. A. R. Monzo characterized semilattices of rectangular bands and groups of exponent 2. However, his characterization does not seem to point directly to the properties of rectangular bands and groups of exponent 2 (namely, idempotency and commutativity). In this talk I am going to show a natural characterization of these semigroups. This research was carried out under the supervision of Professor Michael Kinyon from Denver University.