Finite abundant semigroups in which the idempotents form a subsemigroup

Journal of Algebra, 295 (2006), 303-313


We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pdeudovarieties of finite groups and finite aperiodic semigroups.