Geodesic
Embedding any countable semigroup in a 2-generated bisimple monoid
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 153-161

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G. B. Preston [10] proved that any semigroup can be embedded in a bisimple monoid. If S is a countable semigroup, his constructive proof yields a bisimple monoid which is also countable, but not necessarily finitely generated. The main result of this paper is that any countable semigroup can be embedded in a 2-generated bisimple monoid.J. M. Howie [6] proved that any semigroup can be embedded in an idempotentgenerated semigroup. F. Pastijn [9] showed that any semigroup can be embedded in a bisimple idempotent-generated semigroup, and that any countable semigroup can be embedded in a semigroup which is generated by 3 idempotents. Easy proofs of these results using Rees matrix semigroups over a semigroup were given by the author [3]. In this paper, as a corollary to our main result, we deduce that any countable semigroup can be embedded in a bisimple semigroup which is generated by 3 idempotents. 
Byleen, Karl. Embedding any countable semigroup in a 2-generated bisimple monoid. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 153-161. doi: 10.1017/S0017089500005565
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