对称群S_(n)(n≤14)的新刻画  

An New Characterization of Symmetric Groups S_(n)(n≤14)

作　　者：岳念 晏燕雄[1] YUE Nian;YAN Yan-xiong(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2021年第6期1-4,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11171364,11271301);中央高校专项基金项目(XDJK2019C116,XDJK2019B030);西南大学教改项目(2018JY061).

摘　　要：设G是有限群,o_(1)(G)表示G中最高阶元素的阶,n1(G)表示G中最高阶元素的个数.设G一共有r个o_(1)(G)阶元,且中心化子的阶两两不同,并依次设这些中心化子的阶为c_(1)(G),c_(2)(G),…,cr(G).令ONC1(G)={o_(1)(G);n1(G);c_(1)(G),c_(2)(G),…,cr(G)},称为G的第一ONC度量.本文得到:设G为有限群且G的素图不连通,则G■S_(n)(n≤14)当且仅当ONC_(1)(G)=ONC_(1)(Sn).Let G be a finite group,o_(1)(G)denote the largest element order of G,and n1(G)denote the number of the element of order o_(1)(G).Assume that G totally has r elements of order o_(1)(G),of which the centralizers are of different orders,and ci(G)denote the order of centralizer of i the element of order o_(1)(G)(i=1,2,…,r).Define ONC1(G)={o_(1)(G);n1(G);c_(1)(G),c_(2)(G),…,cr(G)}.We call ONC1(G)the 1st ONC-degree of G.In this article it is proved that let G be a finite group and the prime graph of G is not connected,then G■S_(n)(n≤14)if and only if ONC_(1)(G)=ONC_(1)(Sn).

关 键 词：有限群 对称群 ONC度量 素图 

分 类 号：O152.1[理学—数学]