On the rational subset problem for groups

• Type: Article in International Scientific Journal
• Date: 2007

Authors

Mark Kambites (Author) Other; Pedro V. Silva (Author) FCUP; Benjamin Steinberg (Author) Other

Journal

Title: Journal of Algebra

Vol. 309

Pages: 622-639

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 27 Citations

ISI Web of Science

Scopus - 34 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-004-B5N

DOI: 10.1016/j.jalgebra.2006.05.020

Abstract (EN): We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automaton subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18