The equation x(i)=y(j)z(k) in a free semigroup

: Harju T, Nowotka D

Publisher: SPRINGER-VERLAG

: 2004

Semigroup Forum

SEMIGROUP FORUM

: SEMIGROUP FORUM

: 68

: 3

: 488

: 490

: 3

: 0037-1912

DOI: https://doi.org/10.1007/s00233-003-0028-6

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.

Mathematics