Geodesic
Some Properties of Periodic Words
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 330-337

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, it is proved that the cube of a simple word cannot be decomposed into the product of words with periods of smaller length. In addition, the decomposition of a simple word's square into the product of words with shorter periods is studied. The interest in this sort of statements stems from the investigation of groups and semigroups specified by periodic defining relations. 
@article{MZM_2002_72_3_a1,
     author = {V. S. Guba},
     title = {Some {Properties} of {Periodic} {Words}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {330--337},
     publisher = {mathdoc},
     volume = {72},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a1/}
}
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V. S. Guba. Some Properties of Periodic Words. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 330-337. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a1/