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Some non finitely generated monoids of repetition-free endomorphisms

✍ Scribed by G. Richomme

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
99 KB
Volume
85
Category
Article
ISSN
0020-0190

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✦ Synopsis

We answer a question raised by Mitrana in Information Processing Letters 64 about primitive morphisms, that is, morphisms that preserve primitiveness of words. Given an alphabet A with Card(A) 2, the monoid of primitive endomorphisms on A and the monoid of primitive uniform endomorphisms on A are not finitely generated. Moreover we show that it is also the case for the following monoids: the monoid of overlap-free (uniform) endomorphisms on A (when Card(A) 3), the monoid of k-power-free (uniform) endomorphisms on A (when Card(A) 2 and k 3).

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