Geodesic
A Characterization of the Commutator Subgroup of a Group
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 93-94

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An element a of a semigroup S is n-potent if there exist a 1, a 2,..., a k ∈S such that a = a 1 a 2...a k and If S is a group, the set of n-potent elements is a normal subgroup of S and the set of 1-potent elements is the commutator subgroup of S. 
Thierrin, G. A Characterization of the Commutator Subgroup of a Group. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 93-94. doi: 10.4153/CMB-1976-013-2
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[1] 1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 2, Math. Survey 7, Amer. Math. Soc. 1967. Google Scholar

[2] 2. Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41, 1966, 707–716. Google Scholar

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