Cone types and geodesic languages for lamplighter groups and Thompson's group F
Cone types and geodesic languages for lamplighter groups and Thompson's group F
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点灯者组和 Thompson 组 F 的锥体类型和测地线语言
DOI：
10.1016/j.jalgebra.2005.11.016
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发表时间：
2004
影响因子：
0.9
通讯作者：
J. Taback
中科院分区：
文献类型：
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作者：
S. Cleary;M. Elder;J. Taback
我们研究了Lamplighter群和Thompson群F中测地线的语言。我们表明，lampighter组Ln有无穷多个锥类型，没有定期测地线语言，并有1-计数器，上下文无关和计数器测地线语言关于某些生成集。我们表明，完整的语言的测地线相对于一个发电机组的点灯组不是计数器，但上下文无关，而相对于另一个发电机组的完整的语言的测地线是计数器和上下文无关。在汤普森的群F关于标准有限生成集，我们表明有无穷多个锥类型，并没有正规语言的测地线。我们表明，存在的家庭的“跷跷板”元素相对于一个给定的生成集在一个生成的无限群排除了一个正规的语言测地线和保证无限多的锥类型相对于该生成集。
We study languages of geodesics in lamplighter groups and Thompson's group F. We show that the lamplighter groups Lnhave 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.
理查德·汤普森的F组
DOI：
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发表时间：
2015
期刊：
影响因子：
--
作者：
Masaaki Harada;Akihiro Munemasa;Hiroshi Nozaki and Sho Suda;篠原雅史;須田庄;野崎寛;野崎寛;宗政昭弘;須田庄;篠原雅史;宗政昭弘;篠原雅史;篠原雅史;三枝崎剛;野崎寛;篠原雅史;篠原雅史;須田庄;篠原雅史;篠原雅史;野崎寛;宗政昭弘;宗政昭弘;宗政昭弘;篠原雅史;別宮耕一;須田庄;別宮耕一;宗政昭弘
通讯作者：
宗政昭弘