We study a model of computation where executing a program on an input corresponds to calculating a product in a finite monoid. We show that in this model, the subsets of {0,1}^n that can be recognized by nilpotent groups have exponential cardinality.

Translator's note: This is a translation of the article ``Sur les langages reconnus par des groupes nilpotents,'' C. R. Acad. Sci. Paris, t. 306, Serie I, p. 93-95, 1988. It was translated in 1998 with permission from the authors by Alexander and Sarah Russell.