Bourbaki

Exercise 9, § 7

Algebra, I, p. 144

Let x, y in X, such that x≠yx \neq y. Now prove that the submonoid of Mo(X) generated by {x,xy,yx}\{x, xy, yx\} is not isomorphic to a free monoid.

Solution

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Machine translation of the English, by gpt-5-6-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.