Finiteness results for subgroups of finite extensions

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Pedro V. Silva (Author) FCUP; Vítor Araújo (Author) Other; Mihalis Sykiotis (Author) Other

Journal

Title: Journal of Algebra

Vol. 423

Pages: 592-614

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-009-Y2W

DOI: 10.1016/j.jalgebra.2014.10.033

Abstract (EN): We discuss in the context of finite extensions two classical theorems of Takahasi and Howson on subgroups of free groups. We provide bounds for the rank of the intersection of subgroups within classes of groups such as virtually free groups, virtually nilpotent groups or fundamental groups of finite graphs of groups with virtually polycyclic vertex groups and finite edge groups. As an application of our generalization of Takahasi's Theorem, we provide a uniform bound for the rank of the periodic subgroup of any endomorphism of the fundamental group of a given finite graph of groups with finitely generated virtually nilpotent vertex groups and finite edge groups.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23