特征标次数图是一种连通图的单群

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.

Finite Simple Groups with a Kind of Connected Irreducible Character Degrees Graphs

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.