Sylow p-子群为循环群的10pn阶非交换群的 Coleman自同构群
On Coleman Outer Automorphism Groups of Non-Commutative Groups of Order 10pn with Sylow p-Subgroup Being Cyclic Groups
DOI: 10.12677/PM.2021.118165, PDF, HTML, 下载: 340  浏览: 512  国家自然科学基金支持
作者: 依火阿呷*, 海进科#:青岛大学数学与统计学院,山东 青岛
关键词: 射影极限Coleman自同构群内自同构群Projection Limit Coleman Automorphism Inner Automorphism
摘要: 在这篇文章中,利用群的射影极限性质给出了一类Sylow p-子群为循环群的10pn阶非交换群的Coleman自同构群的结构。
Abstract: In this note, we use the projection limit property of groups to give the structure of Coleman automorphism groups for a class of non-commutative groups of order 10pn with Sylow p-subgroup being cyclic groups.
文章引用:依火阿呷, 海进科. Sylow p-子群为循环群的10pn阶非交换群的 Coleman自同构群[J]. 理论数学, 2021, 11(8): 1475-1481. https://doi.org/10.12677/PM.2021.118165

参考文献

[1] Dade, E.C. (1975) Sylow-Centralizing Sections of Outer Automorphism Groups of Finite Groups Are Nilpotent. Mathematische Zeitschrift, 141, 57-76.
https://doi.org/10.1007/BF01236984
[2] Hertweck, M. and Kimmerle, W. (2002) Coleman Automorphisms of Finite Groups. Mathe- matische Zeitschrift, 242, 203-215.
https://doi.org/10.1007/s002090100318
[3] Van Antwerpen, A. (2018) Coleman Automorphisms of Finite Groups and Their Minimal Normal Subgroups. Journal of Pure and Applied Algebra, 222, 3379-3394.
https://doi.org/10.1016/j.jpaa.2017.12.013
[4] 赵文英, 海进科. 关于有限内幕零群和Frobenius群的Coleman自同构[J]. 山东大学学报(理学 版), 2017, 52(10): 4-6.
[5] Kimmerle, W. and Roggenkamp, K.W. (1993) Projective Limits of Group Rings. Journal of Pure and Applied Algebra, 88, 119-142.
https://doi.org/10.1016/0022-4049(93)90017-N
[6] 吴洪毅, 海进科. 广义二面体群的Coleman自同构群[J]. 山东大学学报(理学版), 2020, 55(12): 37-39.
[7] 吉晓娟, 周伟. Sylow p-子群为循环群的10pn阶非交换群的非交换群[J]. 西南大学学报(自然科 学版), 2013, 35(10): 56-59.
[8] 海进科, 吕瑞珍. Coleman自同构群的投射极限[J]. 数学学报, 2020, 63(4): 281-288.
[9] 徐明耀. 有限群导寻[M]. 北京: 科学出版社, 1999.
[10] Hai, J.K. and Zhu, Y.X. (2018) On Coleman Automorphisms of Extensions of Finite Quasinilpotent Groups by Some Groups. Algebra Colloquium, 25, 181-188.
https://doi.org/10.1142/S1005386718000123