On finite-index extensions of subgroups of free groups

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Pedro V. Silva (Author) FCUP; Pascal Weil (Author) Other

Journal

Title: Journal of Group Theory

Vol. 13 No. 3

Pages: 365-381

ISSN: 1433-5883

Publisher: Walter De Gruyter

Indexing

ISI Web of Knowledge - 1 Citation

ISI Web of Science

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-726

DOI: 10.1515/jgt.2009.055

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17