A1 Refereed original research article in a scientific journal
The equation x(i)=y(j)z(k) in a free semigroup
Authors: Harju T, Nowotka D
Publisher: SPRINGER-VERLAG
Publication year: 2004
Journal:: Semigroup Forum
Journal name in source: SEMIGROUP FORUM
Journal acronym: SEMIGROUP FORUM
Volume: 68
Issue: 3
First page : 488
Last page: 490
Number of pages: 3
ISSN: 0037-1912
DOI: https://doi.org/10.1007/s00233-003-0028-6
Abstract
The equation x(i) = y(j)z(k) has only periodic solutions in a free semigroup. This result was first proven by Lyndon and Schutzenberger. We present a very short proof of this classical result. Moreover, we establish that the power of two or more of a primitive word cannot be factorized into conjugates of a different word.
The equation x(i) = y(j)z(k) has only periodic solutions in a free semigroup. This result was first proven by Lyndon and Schutzenberger. We present a very short proof of this classical result. Moreover, we establish that the power of two or more of a primitive word cannot be factorized into conjugates of a different word.
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