Cone types and geodesic languages for lamplighter groups and Thompson's group F

JOURNAL OF ALGEBRA

卷:303

Article

Cleary, Sean ; Elder, Murray ; Taback, Jennifer

关键词: regular language;    rational growth;    cone type;    context-free grammar;    counter automata;    lamplighter groups;    Thompson's group F;   

DOI  :  10.1016/j.jalgebra.2005.11.016

来源: Elsevier

【 摘 要 】

We study languages of geodesics in lamplighter groups and Thompson's group F. We show that the lamplighter groups L, have infinitely many cone types, have no regular geodesic languages, and have 1-counter, context-free and counter geodesic languages with respect to certain generating sets. We show that the full language of geodesics with respect to one generating set for the lamplighter group is not counter but is context-free, while with respect to another generating set the full language of geodesics is counter and context-free. In Thompson's group F with respect to the standard finite generating set, we show there are infinitely many cone types and that there is no regular language of geodesics. We show that the existence of families of seesaw elements with respect to a given generating set in a finitely generated infinite group precludes a regular language of geodesics and guarantees infinitely many cone types with respect to that generating set. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free