Geodesic
Cancellative actions
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 399-411.

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The following problem is considered: when can the action of a cancellative semigroup $S$ on a set be extended to a simply transitive action of the universal group of $S$ on a larger set.
Classification : 18B40, 20M20, 20M30, 20M50
Keywords: semigroup action; monoid action; cancellative action; universal actions; $S$-set; tensor product 
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Grillet, Pierre Antoine. Cancellative actions. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a1/