On the structure of semigroups which are unions of groups
R. J. Warne · Transactions of the American Mathematical Society · 1973
We characterize semigroups S which are unions of groups as generalized Schreier products of groups, semilattices of right zero semigroups, and semilattices of left zero semigroups. We then give several specializations of this result utilizing Schreier products, semidirect products, and direct products.