On finite-index extensions of subgroups of free groups
Silva, Pedro ; Weil, Pascal
arXiv, 0808.2381 / Harvested from arXiv
Text on arXiv
We study the lattice of finite-index extensions of a given finitely generated subgroup $H$ of a free group $F$. This lattice is finite and we give a combinatorial characterization of its greatest element, which is the commensurator of $H$. This characterization leads to a fast algorithm to compute the commensurator, which is based on a standard algorithm from automata theory. We also give a sub-exponential and super-polynomial upper bound for the number of finite-index extensions of $H$, and we give a language-theoretic characterization of the lattice of finite-index subgroups of $H$. Finally, we give a polynomial time algorithm to compute the malnormal closure of $H$.
Publié le : 2008-08-18
Classification:  Mathematics - Group Theory,  20E05 
@article{0808.2381,
     author = {Silva, Pedro and Weil, Pascal},
     title = {On finite-index extensions of subgroups of free groups},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0808.2381}
}

Silva, Pedro; Weil, Pascal. On finite-index extensions of subgroups of free groups. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0808.2381/