摘要
本文首先通过计算给出了对称群Sn(n≤15)的阶|Sn|,最高阶元的阶k1(Sn),次高阶元的阶k2(Sn)及第三高阶元的阶k3(Sn)。然后利用有限单群分类定理证明了Sn(n=1,2,…,9,11,13,14)可由|Sn|和k1(Sn)刻画,即有限群G同构于Sn当且仅当|G|=|Sn|且k1(G)=k1(Sn)。最后对Sn(n=10,12,15)证明了它们可由|Sn|和k1(Sn),k2(Sn)及k3(Sn)刻画,即G同构于Sn当且仅当|G|=|Sn|且k1(G)=k1(Sn),k2(G)=k2(Sn)及k3(G)=k3(Sn)。
First, in this paper, we get the order of S. (n≤ 15), the largest element order k1 (Sn), the second largest element order k2 (Sn), and the third largest element order k3 (Sn) by calculation. Second, using the classification theorem of finite simple groups, we prove that S.(n=1,2,…,9,11,13,14)can be characterized by |Sn|and kl (Sn),namely , a finite group G is isomorphic to Sn if and only if |G| = | Sn |and kl (G) = k1 (Sn). Finally, we prove that S. (n= 10,12,15) an be characterized by |Sn| and k1 (S.), k2 (Sn), k3 (Sn),that is, a finite group G is isomorphic to S. if and only if |G| = |Sn| and k1(G) = k1(Sn), k2(G) = k2(Sn), k3(G) = k3(Sn).
出处
《重庆师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2013年第6期81-85,共5页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.11271301)
中央高校基本科研业务费专项资金(No.XDJK2012D004)
关键词
有限群
对称群
最高阶元的阶
次高阶元的阶
finite group
symmetric groups
the largest element order
the second largest element order