S_(10)的非交换图刻画

Noncommuting Graph Characterization of S_(10)

探讨了用非交换图刻画有限单群的AAM猜想,利用非交换图的性质,极大可解正规子群的特点,得到正规群列,再借助素因子不超过7的有限单群分类及扩张理论,得到了主要结论:10个点上的对称群S10可以用非交换图刻画.该刻画问题进一步完善了AAM猜想的内容,同时借助此方法,还可以解决单个单群或几乎单群的非交换图刻画问题.

AAM conjecture about characterization of the finite simple groups by their non-commuting graphs was investigated.Using the properties of non-commuting graph,the specialties of maximal solvable normal subgroup,a normal serie was built.And according to the classification of finite simple groups with prime factors less than 7and extension theorem,the main result was proved,that was,S10,the symmetric group with more than 10 degrees,can be charactered by its noncommuting graph.The characterization problem further improved the content of the AAM conjecture.And using this method,at the same time,the single simple group or almost all simple groups can also be solved.