On finite-index extensions of subgroups of free groups

Details On finite-index extensions of subgroups of free groups On finite-index extensions of subgroups of free groups

2008-08-18

arxiv.org/abs/0808.2381v2

Journal of Group Theory 13, 3 (2010) 365-381

Mathematics

Group Theory

Scientific paper

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 $H$.

Affiliated with

Also associated with

No associations

Rating

On finite-index extensions of subgroups of free groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On finite-index extensions of subgroups of free groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On finite-index extensions of subgroups of free groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697880