Visual decompositions of Coxeter groups
Visual decompositions of Coxeter groups
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Coxeter 群的视觉分解
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Tschantz
中科院分区：
文献类型：
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作者：
M. Mihalik;S. Tschantz
Coxeter系统是一个有序对W;S/，其中S是Coxeter群W的特定表示类型的生成集。如果W的子群是由S的子集生成的，则称W的子群是特殊子群。从Coxeter群的表示中可以很容易地识别出具有特殊因子和特殊合并子群的Coxeter群的合并积分解。如果一个考克斯特群是一个给定群的图的基本群的子群，那么考克斯特群也是一个特殊子群的图的基本群，其中每个顶点和边群是给定群的图的顶点或边群的共轭的子群。证明了Coxeter群的群分解的任意图的顶点群分裂为与特殊群共轭的部分和给定分解的边群的子群的部分。主要定理的几个应用，包括分类的最大FA子群的一个可再生Coxeter群的某些特殊子群的所有共轭。数学学科分类（2000）。20F55 20E08 20E28
A Coxeter system is an ordered pair .W;S/ where S is the generating set in a particular type of presentation for the Coxeter groupW . A subgroup ofW is called special if it is generated by a subset ofS. Amalgamated product decompositions of a Coxeter group having special factors and special amalgamated subgroup are easily recognized from the presentation of the Coxeter group. If a Coxeter group is a subgroup of the fundamental group of a given graph of groups, then the Coxeter group is also the fundamental group of a graph of special subgroups, where each vertex and edge group is a subgroup of a conjugate of a vertex or edge group of the given graph of groups. A vertex group of an arbitrary graph of groups decomposition of a Coxeter group is shown to split into parts conjugate to special groups and parts that are subgroups of edge groups of the given decomposition. Several applications of the main theorem are produced, including the classification of maximal FA subgroups of a finitely generated Coxeter group as all conjugates of certain special subgroups. Mathematics Subject Classification (2000). 20F55, 20E08, 20E28.