交错群的谱可识别性
Recognizability by spectrum of alternating groups
摘要：
一个群的谱是它的元素阶的集合。一个有限群$G$称为可谱识别的，如果每个与$G$具有相同谱的有限群都同构于$G$。证明了当$n\neq 6, 10$是单交错群时，单交错群$A_n$是谱可识别的.这意味着每个与有限非交换单群具有相同谱的有限群至多有一个非交换合成因子
英文摘要：
The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group that has the same spectrum as $G$ is isomorphic to $G$. We prove that the simple alternating groups $A_n$ are recognizable by spectrum when $n\neq 6, 10$. This implies that every finite group with the same spectrum as that of a finite nonabelian simple group, has at most one nonabelian composition factor
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