Symmetry groups of vertex-transitive polytopes
Symmetry groups of vertex-transitive polytopes
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顶点传递多胞形的对称群
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
L. Babai
中科院分区：
文献类型：
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作者：
L. Babai
不同构于任何顶点可迁多面体（任何维数）的对称群的群被刻画为广义双循环群或阿贝尔群，但不是初等2-群。同一类群G的特征还在于存在作用于G的置换群P，包含G *（G的正则表示）作为真子群，使得单位ε G的稳定子Pu的成员取每g ε G为g ±1。
Groups which are not isomorphic to the symmetry group of any vertextransitive polytope (of any dimension) are characterized as generalized dicyclic, or abelian groups but not elementary 2-groups. The same class of groupsG is also characterized by the existence of a permutation groupP acting onG, containingG* (the regular representation ofG) as a proper subgroup, such that the members of the stabilizerPu of the unitu ε G take everyg ε G tog±1.