On the rational subset problem for groups

• Tipo: Artigo em Revista Científica Internacional
• Data: 2007

Autores

Mark Kambites (Autor) Outra; Pedro V. Silva (Autor) FCUP; Benjamin Steinberg (Autor) Outra

Revista

Título: Journal of Algebra

Vol. 309

Páginas: 622-639

ISSN: 0021-8693

Editora: Elsevier

Indexação

ISI Web of Knowledge - 27 Citações

ISI Web of Science

Scopus - 34 Citações

Classificação Científica

FOS: Ciências exactas e naturais

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 18