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Finite abundant semigroups in which the idempotents form a subsemigroup

Fountain, John B.; Gomes, Gracinda M. S.

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.