具有某种扩张的有限群的Coleman自同构

doi:10.6040/j.issn.1671-9352.0.2018.673

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (10): 109-112.doi: 10.6040/j.issn.1671-9352.0.2018.673

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具有某种扩张的有限群的Coleman自同构

赵乐乐,海进科^*

青岛大学数学与统计学院, 山东青岛 266071

发布日期:2019-10-12
作者简介:赵乐乐(1995— ),女,硕士研究生,研究方向为有限群理论及其表示. E-mail:1944024728@qq.com *通信作者简介:海进科(1964— ),男,博士,教授,研究方向为有限群理论及其表示. E-mail:haijinke2002@aliyun.com
基金资助:
国家自然科学基金资助项目(11871292)

Coleman automorphisms of extensions of the finite groups by some groups

ZHAO Le-le, HAI Jin-ke^*

College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China

Published:2019-10-12

摘要/Abstract

摘要： 设G是有限特征单群被有限交换群或有限非交换单群的扩张,证明了G的每个Coleman自同构均为内自同构。

关键词: 特征单群, Coleman自同构, 内自同构

Abstract: Let G be an extension of a finite characteristically simple group by a finite abelian group or a finite non-abelian simple group. It is shown that under some conditions all Coleman automorphism of G is an inner automorphism.

Key words: characteristically simple group, Coleman automorphism, inner automorphism

中图分类号:

O152.6

赵乐乐,海进科. 具有某种扩张的有限群的Coleman自同构[J]. 《山东大学学报(理学版)》, 2019, 54(10): 109-112.

ZHAO Le-le, HAI Jin-ke. Coleman automorphisms of extensions of the finite groups by some groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 109-112.

参考文献

[1] DADE E C. Sylow-centralizing sections of outer automorphism groups of finite groups are nilpotent[J]. Mathematische Zeitschrift, 1975, 141(1):57-76.
[2] HERTWECK M, KIMMERLE W. Coleman automorphisms of finite groups[J]. Mathematische Zeitschrift, 2002, 242(2):203-215.
[3] HAI Jinke, ZHU Yixin. On Coleman automorphisms of extensions of finite quasinilpotent groups by some groups[J]. Algebra Colloquium, 2018, 25(2):181-188.
[4] ANTWERPEN A V. Coleman automorphisms of finite groups and their minimal normal subgroups[J]. Journal of Pure and Applied Algebra, 2018, 222(11):3379-3394.
[5] 赵文英,海进科.关于有限内幂零群和Frobenius群的Coleman自同构[J]. 山东大学学报(理学版),2017,52(10):4-6. ZHAO Wenying, HAI Jinke. On Coleman automorphism of finite inner nilpotent groups and Frobenius groups[J]. Journal of Shandong University(Natural Science), 2017, 52(10):4-6.
[6] KURZWEIL H,STELLMACHER B. The theory of finite groups[M]. Berlin: Springer-Verlag, 2004.
[7] 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. HAI Jinke, WANG Wei, HE Weiping. A note on Coleman automorphism of finite groups[J]. Journal of Shandong University(Natural Science), 2016, 51(4):35-38.
[8] HERTWECK M. Class-preserving automorphisms of finite groups[J]. Journal of Algebra, 2001, 241(1):1-26.
[9] ROSE J S. A course on group theory[M]. Cambridge: Cambridge University Press, 1978.

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具有某种扩张的有限群的Coleman自同构

Coleman automorphisms of extensions of the finite groups by some groups

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[1]	赵文英,海进科. 关于有限内幂零群和Frobenius群的Coleman自同构[J]. 山东大学学报（理学版）, 2017, 52(10): 4-6.
[2]	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.