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A Proof of Shirshov's Theorem

✍ Scribed by Giuseppe Pirillo

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 188 KB
Volume: 124
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1996.0079

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✦ Synopsis

Sane copiosam tu et uberem messem ex hoc agro collegisti, nos pauculas spicas contemptas tibi potius quam non visas.

Triumphus igutur hic omnis tuus est: mihi abunde satis si armillis aut hasta donatus, sequar hunc candidae famae tuae currum.

wJustus Lipsius

In this paper we prove that, except for at most one, all the ranks of a right infinite word which is recurrent and not ultimately periodic are the starting point of an |-division. Using this we give a very simple proof of Shirshov's theorem. We also extend it to not necessarily finite alphabets.

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