Structure of finite simple groups and applications of the classification of finite simple groups

研究了有限简单群的结构，利用有限简单群的分类得到了有限简单群的几个性质。Yamaki证明了71.35或L_2（71）是Monster的极大子群，并利用素数图研究了有限简单群的奇阶极大子群。Iiyori与Seichi Abe一起定义了有限群的可解图，并研究了有限简单群图的结构。除此之外，他们证明了有限单群的图是连通的而不是完备的。利用图的这些性质，推广了有限群可解性的P. Hall定理。Sawabe构造了一个新的p局部几何，它包含了零星单群上的几个几何。他和大阪大学的Uno证实了Dade对里昂-西姆斯单群的猜想。Sawabe和Watanabe证明了具有素数惯性指标的主块的Alperin权猜想。Chigira研究了Bender-Glauberman关于奇阶群可解性的书，并用Peterfalvi的奇阶群特征理论简化了Suzuki的上一篇论文。

We studied about the structures of finite simple groups and found several properties of finite groups using the classification of finite simple groups.Yamaki proved that either 71 : 35 or L_2(71) is a maximal subgroup of the Monster and studied about odd order maximal subgroups of finite simple groups using prime graphs.Iiyori defined solvable graphs of finite groups with Seichi Abe and studied about the structure of the graphs of finite simple groups. Among other things they proved that the graphs of finite simple groups are connected and not complete. Using these properties of graphs Iiyori generalized P. Hall's theorem on the solvability of finite groups.Sawabe constructed a new p-local geometry which includes several geometries on the sporadic simple groups. He and Uno(0saka University) verified Dade's conjecture for the Lyons-Sims simple groups. Sawabe and Watanabe proved the Alperin's weight conjecture for the principal block with prime inertia index.Chigira studied Bender-Glauberman's book on the solvability of groups of odd order and simplified Suzuki's last paper using Peterfalvi's character theory for the groups of odd order.