کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414082 | 1333801 | 2013 | 17 صفحه PDF | دانلود رایگان |

Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive (possibly infinite) presentation, a so-called finite L-presentation. Finite L-presentations allow numerous algorithms for finitely presented groups to be generalized to this special class of recursive presentations. We give an overview of the algorithms for finitely L-presented groups. As applications, we demonstrate how their implementation in a computer algebra system allows us to study explicit examples of self-similar groups including the Fabrykowski-Gupta groups and the Grigorchuk group. Our experiments yield detailed insight into the structure of these groups.
Journal: Expositiones Mathematicae - Volume 31, Issue 4, 2013, Pages 368-384