  An infinite word, which is aperiodic and codes the orbit of a transformation
of the exchange of three intervals is called 3iet word. Such a word is thus a
natural generalization of a sturmian word to a word over 3-letter alphabet. A
morphism is said to be 3iet preserving if it maps any 3iet word to another 3iet
word. It is known that the monoid of morphisms preserving sturmian words is
finitely generated. On the contrary, in this note we prove that the monoid of
3iet preserving morphisms is not finitely generated, that is, there are
infinitely many 3iet preserving morphisms, which cannot be written as a
non-trivial decomposition of other 3iet preserving morphisms.
