特征标次数图是一种连通图的单群 |
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引用本文: | 梁登峰. 特征标次数图是一种连通图的单群[J]. 数学的实践与认识, 2014, 0(24) |
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作者姓名: | 梁登峰 |
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作者单位: | 北京工商大学理学院; |
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基金项目: | 北京工商大学青年教师科研启动基金资助项目(QNJJ2013-24) |
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摘 要: | 对有限单群G,假设其不可约特征标次数图Δ(G)连通,且图顶点集ρ(G)=π_1∪π_2∪{p},其中|π_1|,|π_2|≥1,π_1∩π_2=θ,且π_1与π_2中顶点不相邻.证明了Δ(G)满足上面的假设的有限单群G只有4种:M_(11),J_1,PSL_3(4)或2B_2(q2B_2(q2),其中q2),其中q2一1是Mersenne素数.
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关 键 词: | 有限单群 不可约特征标次数素图 连通图 |
Finite Simple Groups with a Kind of Connected Irreducible Character Degrees Graphs |
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Abstract: | In the paper we get the conclusion:Let G be a finite simple group,A(G)has only one conneced component,and ρ(G) = π_1 ∪ π_2 ∪{p} 's disjoint union,where |π_1|,|π_2| > 1,π_1 ∩ π_2 = 0.Assume that no prime in π_1 is adjacent in A(G) to any prime in π_2.Then G is one of the groups:M_(11),J_1,PSL_3(4) or ~2B_2(q~2),where q2- 1 is a Mersenne prime. |
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Keywords: | finite simple groups irreducible character degrees graphs connected graph |
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