On uniformly repetitive semigroups |
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| Authors: | G Pirillo S Varricchio |
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| Institution: | (1) IAMI-CNR Sezione di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy;(2) Dipartimento di Matematica, Università di Catania, Viale A. Doria 6, 90125 Catania, Italy |
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| Abstract: | Letk be an integer greater than 1 andS be a finitely generated semigroup. The following propositions are equivalent: 1) the semigroup of non negative integers is
not uniformlyk-repetitive; 2) any finitely generated and uniformlyk-repetitive semigroup is finite. As a consequence we prove that any finitely generated and uniformly 4-repetitive semigroup
is finite. |
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