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有限群的一类新的共轭类图 被引量:1

A new graph of conjugacy classes of finite groups
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摘要 定义了有限群G的一类新的共轭类图Γ(G):它以G的非中心的共轭类为顶点,不同的顶点xG和yG之间有一条边相连当且仅当它们的代表元的阶有非平凡的公因子.令n(G)和diam(Γ(G))分别表示Γ(G)的连通分支数和直径,证明了对任意有限群G,n(G)≤6和diam(Γ(G))≤6. A new graph Γ(G) of conjugacy classes of a finite group G was defined, its vertices are the non-central conjugacy classes of G and two distinct vertices x^G and y^G are connected with an edge if and only if the orders of their representative elements have a nontrivial common divisor. Let n(G) and diam (Γ(G)) be the number of connected components and the diameter of Γ(G), respectively. We prove that n(G) 46 and diam (Γ(G)) 46 for any finite group G.
作者 游兴中
出处 《长沙理工大学学报(自然科学版)》 CAS 2007年第3期87-88,92,共3页 Journal of Changsha University of Science and Technology:Natural Science
基金 国家自然科学基金资助项目(10671026) 长沙理工大学科研资助项目(1004116)
关键词 有限群 共轭类图 连通分支数 直径 单群 finite group graph of conjugacy classes number of connected component diameter simple group
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参考文献8

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二级参考文献11

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