Soluble Semigroups
Peter G. Trotter · Journal of the Australian Mathematical Society · 1972
The cancellation law is a necessary condition for a semigroup to be embedded in a group. In general, this condition is not sufficient; necessary and sufficient conditions are rather complicated (see [1]). It is, therefore, of interest to find large classes of semigroups for which the cancellation law is sufficient to ensure embeddability in a group.