Geodesic
Free Involutorial Completely Simple Semigroups
Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 271-295

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An involution x → x* of a semigroup S is an antiautomorphism of S of order at most 2, that is (xy)* = y*x* and x** = x for all x, y ∊ S. In such a case, S is called an involutorial semigroup if regarded as a universal algebra with the binary operation of multiplication and the unary operation *. If S is also a completely simple semigroup, regarded as an algebra with multiplication and the unary operation x → x −1 of inversion (x −1 is the inverse of x in the maximal subgroup of S containing x), then (S, −1, *), or simply S, is an involutorial completely simple semigroup. All such S form a variety determined by the identities above concerning * and where x 0 = xx −1. 
Gerhard, J. A.; Petrich, Mario. Free Involutorial Completely Simple Semigroups. Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 271-295. doi: 10.4153/CJM-1985-017-9
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