On syntactic groups
Perrin, Dominique ; Rindone, Giuseppina
Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 749-759 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We prove that for any finite prefix code $X$ with $n$ elements, the non special subgroups in the syntactic monoid of $X^*$ have degree at most $n-1$. This implies in particular that the groups in the syntactic monoid of $X^*$ are all cyclic when $X$ is a prefix code with three elements.
Publié le : 2003-12-14
Classification:  variable-length codes,  syntactic monoids,  finite groups,  20M05,  68R15 
@article{1074791330,
     author = {Perrin, Dominique and Rindone, Giuseppina},
     title = {On syntactic groups},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 749-759},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1074791330}
}

Perrin, Dominique; Rindone, Giuseppina. On syntactic groups. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  749-759. http://gdmltest.u-ga.fr/item/1074791330/