《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (11): 32-36.doi: 10.6040/j.issn.1671-9352.0.2025.014
• • 上一篇
白一曼1,海进科1,2*
BAI Yiman1, HAI Jinke1,2*
摘要： 设n是一个整数(正、负或零),证明2个有限n-可解群H和K生成的群〈H,K〉在其中一个子群是次正规条件下仍是有限n-可解群。证明如果有限群G的所有非n-幂零真子群皆次正规且n-可解,则G是n-可解群。
中图分类号:
| [1] HAWTHORN I, GUO Y. Arbitrary functions in group theory[J]. New Zealand Journal of Mathematics, 2015, 45(1):1-9. [2] POTT A. Finite geometry and character theory[M]. Berlin: Springer, 1995. [3] BAER R. Factorization of n-soluble and n-nilpotent groups[J]. Proceedings of the American Mathematical Society, 1953, 4:15-26. [4] HAWTHORN I. Nil series from arbitrary functions in group theory[J]. Commentationes Mathematicae Universitatis Carolinae, 2018, 59(1):1-13. [5] 姜久亮. 关于n-可解群与n-幂零群的两个结果[J]. 数学杂志,1997, 17(4):445-449. JIANG Jiuliang. Two results of n-soluble group and n-nilpotent group[J]. Journal of Mathematics(PRC), 1997, 17(4):445-449. [6] WIELANDT H. Über Produkte von nilpotenten gruppen[J]. Illinois Journal of Mathematics, 1958, 2:611-618. [7] 徐明曜. 有限群导引(上)[M]. 北京:科学出版社,2001. XU Mingyao. Finite groups: an introduction[M]. Beijing: Science Press, 2001. [8] BEIDLEMAN J, HEINEKEN H. Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups[J]. Journal of Group Theory, 2003, 6(2):139-158. [9] CHEN Chanchan, LU Jiakuan, LI Jinbao. Finite groups whose subgroups of even order are TI-subgroups or subnormal subgroups[J]. Advances in Mathematics, 2023, 52(5):883-886. [10] SHI Jiantao. Finite groups in which every non-abelian subgroup is a TI-subgroup or a subnormal subgroup[J]. Journal of Algebra and Its Applications, 2019, 18(8):1950159. [11] ROSE J S. A course on group theory[M]. London: Cambridge University Press, 1978. |
| [1] | 马小箭,毛月梅. 关于有限群中非σ-次正规子群数量的探讨[J]. 《山东大学学报(理学版)》, 2025, 60(5): 9-12. |
|
||
