Diagram Groups
Diagram Groups
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图组
DOI：
10.1090/memo/0620
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发表时间：
1996
影响因子：
--
通讯作者：
M. Sapir
中科院分区：
文献类型：
--
作者：
V. Guba;M. Sapir
图群是由球面图（图片）组成的群。它们也可以被定义为与单群表示相关的Squier配合物的基群。作者证明了图群类包含了一些著名的群，如R. Thompson群f，该类在自由积、有限直积和其他一些群论运算下是封闭的。作者发展了类似于词的组合学的图的组合学。这有助于找到图组的一些结构和算法属性。其中一些性质甚至对于R. Thompson的群F来说也是新的。特别地，作者描述了F中元素的中心子，证明了它具有可解的共轭问题等。
Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group F. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group F. In particular, the authors describe the centralizers of elements in F, prove that it has solvable conjugacy problems, etc.