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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (10): 4-6.doi: 10.6040/j.issn.1671-9352.0.2017.001

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关于有限内幂零群和Frobenius群的Coleman自同构

赵文英,海进科*   

  1. 青岛大学数学与统计学院, 山东 青岛 266071
  • 收稿日期:2016-12-29 出版日期:2017-10-20 发布日期:2017-10-12
  • 通讯作者: 海进科(1964— ),男,博士,教授,研究方向为有限群及其表示.E-mail:haijinke2002@aliyun.com E-mail:1506709601@qq.com
  • 作者简介:赵文英(1992— ),女,硕士研究生,研究方向为有限群及其表示.E-mail:1506709601@qq.com
  • 基金资助:
    山东省自然科学基金资助项目(ZR2016AM21)

On Coleman automorphisms of finite inner nilpotent groups and Frobenius groups

  1. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2016-12-29 Online:2017-10-20 Published:2017-10-12

摘要: 设G是有限群N通过有限群H的半直积。 证明了某些条件下G的每个Coleman自同构均为内自同构。

关键词: 内幂零群, Coleman自同构, Frobenius群, 正规化子问题

Abstract: Let G be a semidirect product of a finite group N by a finite group H. It is shown that under some conditions every Coleman automorphism of G is an inner automorphism.

Key words: normalizer problem, inner nilpotent group, Coleman automorphism, Frobenius group

中图分类号: 

  • O152.6
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[1] 海进科,王伟,何威萍. 关于有限群Coleman自同构的一个注记[J]. 山东大学学报(理学版), 2016, 51(4): 35-38.
[2] 郭继东1,海进科2*. 关于类保持自同构的一个注记[J]. 山东大学学报(理学版), 2014, 49(06): 46-49.
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