极大子群都同构的有限p-群
On Finite p-Groups Whose All Maximal Subgroups are Isomorphic
-
摘要: 设群G是一个有限p-群.如果G的所有极大子群都同构，则称G为MI群.利用正则p-群以及MI群的性质，通过分类讨论的方法，给出了阶不大于p6的MI群的结构.Abstract: A finite p-group is said to be a MI group if all of its maximal subgroups are isomorphic. In this paper, the structure of MI groups whose order is less than or equal to p6 is given by means of the properties of regular p-groups and MI groups.
-
Key words:
- maximal subgroups /
- inner abelian p-group /
- regular p-group .
-
-
[1] HERMANN P Z. On a Class of Finite Groups Having Isomorphic Maximal Subgroups[J]. Ann Univ Sci Budapest Eötvös Sect Math, 1981, 24:87-92. [2] HERMANN P Z. On Finite p-Groups with Isomorphic Maximal Subgroups[J]. J Austral Math Soc, 1990, 48(2):199-213. [3] HERMANN P Z. (MI)-Groups Acting Uniserially on a Normal Subgroup[J]. London Math Soc, 1995, 211:264-268. [4] MANN A. On p-Groups Whose Isomorphic Maximal Subgroups are Isomorphic[J]. J Austral Math Soc, 1995, 59(2):143-147. [5] 孙秀娟. 指数为p2的子群都交换的有限p-群[D]. 临汾:山西师范大学, 2006. [6] 宋蔷薇, 崔双双. 某些MI群[J]. 数学研究, 2011, 44(4):387-392. [7] WANG N E, NEDELA R, HU K. Regular Dessins Uniquely Determined by a Nilpotent Automorphism Group[J]. J Group Theory, 2018, 21(3):397-415. [8] 薛海波. 一类特殊的有限3-群[J]. 西南师范大学学报(自然科学版), 2015, 40(8):7-9. [9] 蹇祥, 吕恒. 具有极大正规化子的有限群[J]. 西南大学学报(自然科学版), 2016, 38(12):56-60. [10] 徐明曜, 曲海鹏. 有限p-群[M]. 北京:北京大学出版社, 2010. [11] BERKOVICH Y. Groups of Prime Power Order[M]. Berlin:Walter de Gruyter, 2008. [12] LV H, ZHOU W, WU H J. Finite p-Groups with Small Subgroups Generated by Two Conjugate Elements[J]. Arch Math, 2013, 100(4):301-308. -
计量
- 文章访问数: 838
- HTML全文浏览数: 691
- PDF下载数: 80
- 施引文献: 0
下载: