Acta Scientiarum Naturalium Universitatis Pekinensis

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Almost Simple DD-groups

LIU Yanjun1, SONG Xueling2, XIONG Huan3   

  1. 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022; 2. Beijing International Center for Mathematical Research, Peking University, Beijing 100871; 3. School of Mathematical Sciences, Peking University, Beijing 100871;
  • Received:2012-09-05 Online:2013-09-20 Published:2013-09-20

几乎单DD-群

刘燕俊1,宋学玲2,熊欢3   

  1. 1. 江西师范大学数学与信息科学学院, 南昌 330022; 2. 北京大学数学国际中心, 北京 100871; 3. 北京大学数学科学学院, 北京 100871;

Abstract: The main purpose is to investigate almost simple DD-groups. It proves that the almost simple group G is not a DD-group unless G is one of the following groups: 1) M22, J2, Co1, Fi'24, McL, Th, B, and the automorphism group of M12 or J2; 2) A5, A6, A7, A9, A10, A16, S5, Aut(A6), S8, S10, or An(62≤n≤205); 3) L3(2), Aut(L3(3)), or L2(q) for q=4, 5, 7, 9, 11.

Key words: almost simple group, multiplicity, degree, DD-group

摘要: 研究几乎单的DD-群, 证明了几乎单群G不是一个DD-群, 如果G不是下列群中的一个: 1) 散在单群M22, J2, Co1, Fi'24, McL, Th, B, 以及M12或者J2的自同构群; 2) 交错群A5, A6, A7, A9, A10, A16, S5, Aut(A6), S8, S10, 或者An(62≤n≤205); 3) L3(2), Aut(L3(3)), 或者L2(q), 其中q=4, 5, 7, 9, 11。

关键词: 几乎单群, 重数, 度数, DD-群

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