کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587528 1334147 2008 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The submonoid and rational subset membership problems for graph groups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The submonoid and rational subset membership problems for graph groups
چکیده انگلیسی

We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is a transitive forest. As a consequence we obtain the first example of a finitely presented group with a decidable generalized word problem that does not have a decidable membership problem for finitely generated submonoids. We also show that the rational subset membership problem is decidable for a graph group if and only if the independence graph is a transitive forest, answering a question of Kambites, Silva, and the second author [M. Kambites, P.V. Silva, B. Steinberg, On the rational subset problem for groups, J. Algebra 309 (2) (2007) 622–639]. Finally we prove that for certain amalgamated free products and HNN-extensions the rational subset and submonoid membership problems are recursively equivalent. In particular, this applies to finitely generated groups with two or more ends that are either torsion-free or residually finite.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 320, Issue 2, 15 July 2008, Pages 728-755