Séminaire Lotharingien de Combinatoire, B26k (1991), 8 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1992, 476/S-26, p.
69-76.]
Giuseppe Pirillo
Properties of Integers and Finiteness Conditions for
Semigroups
Abstract.
Let h and k be integers greater than 1; we prove that
the following statements are equivalent: 1) the direct product of h
copies of the additive semigroup of non-negative integers is not
k-repetitive; 2) if the direct product of h finitely
generated semigroups is k-repetitive, then one of them is finite.
Using this and some results of Dekking and Pleasants on infinite words, we
prove that certain repetitivity properties are finiteness conditions for
finitely generated semigroups.
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