A Classification of Finite Metahamiltonian p-Groups

导出

摘要 A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G.If G is non-nilpotent,then the structure of G has been determined.If G is nilpotent,then the structure of G is determined by the structure of its Sylow subgroups.However,the classification of finite metahamiltonian p-groups is an unsolved problem.In this paper,finite metahamiltonian p-groups are completely classified up to isomorphism.

作者 Xingui Fang Lijian An

机构地区 School of Mathematics Science Department of Mathematics

出处《Communications in Mathematics and Statistics》 SCIE 2021年第2期239-260,共22页 数学与统计通讯（英文）

基金 This work was supported by NSFC(Nos.11971280,11771258).

关键词 Minimal non-abelian groups Hamiltonian groups Metahamiltonian groups A_(2)-groups

分类号 O15 [理学—基础数学]

引文网络
相关文献

参考文献8

1Lijian AN.Finite p-groups whose non-normal subgroups have few orders[J].Frontiers of Mathematics in China,2018,13(4):763-777. 被引量：2
2AN LiJian,LI LiLi,QU HaiPeng,ZHANG QinHai.Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)[J].Science China Mathematics,2014,57(4):737-753. 被引量：10
3QU HaiPeng,XU MingYao,AN LiJian.Finite p-groups with a minimal non-abelian subgroup of index p(Ⅲ)[J].Science China Mathematics,2015,58(4):763-780. 被引量：7
4Qiangwei Song,Haipeng Qu.Finite p-groups whose nonnormal subgroups are metacyclic[J].Science China Mathematics,2020,63(7):1271-1284. 被引量：2
5Qiangwei SONG,Qinhai ZHANG.Finite 2-groups whose length of chain of aonnormal subgroups is at most 2[J].Frontiers of Mathematics in China,2018,13(5):1075-1097. 被引量：1
6Qinhai ZHANG Xiaoxiao LI Meijuan SU.Finite p-groups whose nonnormal subgroups have orders at most p^3[J].Frontiers of Mathematics in China,2014,9(5):1169-1194. 被引量：4
7Qinhai ZHANG,Meijuan SU.Finite 2-groups whose nonnormal subgroups have orders at most 2^3[J].Frontiers of Mathematics in China,2012,7(5):971-1003. 被引量：5
8Qinhai Zhang,Libo Zhao,Miaomiao Li,Yiqun Shen.Finite p-Groups all of Whose Subgroups of Index p^(3) are Abelian[J].Communications in Mathematics and Statistics,2015,3(1):69-162. 被引量：10

二级参考文献35

1An L J, Hu R F, Zhang Q H. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅳ). ArXiv:1310.5503.
2Berkovich Y. Groups of Prime Power Order I. Berlin-New York: Walter de Gruyter, 2008.
3Fang X G, An L J. A classification of finite metahamiltonian p-groups. ArXiv:1310.5509.
4Hall M, Senior J K. The Groups of Order 2n (n≤ 6). New York: MacMillan, 1964.
5Huppert B. Endliche Gruppen I. Berlin: Springer-Verlag, 1967.
6Qu H P, Xu M Y, An L J. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅲ). ArXiv:1310.5496.
7Qu H P, Yang S S, Xu M Y, et al. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅰ). J Algebra,2012, 358: 178-188.
8Qu H P, Zhao L B, Gao J, et al. Finite p-groups with a minimal non-abelian subgroup of index p (V). J Algebra Appl, submitted.
9Tuan H F. A theorem about p-groups with abelian subgroup of index p. Acad Sinica Science Record, 1950, 3: 17-23.
10Xu M Y. An Introduction to Finite Groups (in Chinese). Beijing: Science Press, 1987.

共引文献19

1Qinhai ZHANG Xiaoxiao LI Meijuan SU.Finite p-groups whose nonnormal subgroups have orders at most p^3[J].Frontiers of Mathematics in China,2014,9(5):1169-1194. 被引量：4
2Lihua ZHANG,Yanming XIA,Qinhai ZHANG.Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p[J].Chinese Annals of Mathematics,Series B,2015,36(1):11-30. 被引量：1
3Lijian AN,Le YANG.The Central Extension of an Elementary Abelian p-Group by a Miniaml Non-Abelian p-Group[J].Journal of Mathematical Research with Applications,2016,36(4):457-466.
4Li Fang WANG,Qin Hai ZHANG.Finite p-Groups with a Class of Complemented Normal Subgroups[J].Acta Mathematica Sinica,English Series,2017,33(2):278-286. 被引量：2
5Lijian AN.Finite p-groups whose non-normal subgroups have few orders[J].Frontiers of Mathematics in China,2018,13(4):763-777. 被引量：2
6张军强,郭悦.A_2子群都类3的有限p群[J].山西师范大学学报（自然科学版）,2018,32(3):1-4.
7李伟.三元生成的且A_2群所含内交换子群的个数——限定在A_2群所含交换极大子群小于等于1的情况[J].数学学习与研究,2019(2):138-138.
8Qinhai Zhang.Finite p-Groups Whose Subgroups of Given Order are Isomorphic and Minimal Non-abelian[J].Algebra Colloquium,2019,26(1):1-8. 被引量：1
9Qin Hai ZHANG.Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p^3[J].Acta Mathematica Sinica,English Series,2019,35(7):1179-1189. 被引量：1
10Lifang Wang.Finite p-Groups Whose Number of Subgroups of Each Order Is at most p^4[J].Algebra Colloquium,2019,26(3):411-424.

1Lev Kazarin.Factorizations of Finite Groups and Related Topics[J].Algebra Colloquium,2020,27(1):149-180.
2Yun Miao,Liqun Qi,Yimin Wei.T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product[J].Communications on Applied Mathematics and Computation,2021,3(2):201-220. 被引量：6
3Francesco G. Russo.Problems of Connectivity between the Sylow Graph,the Prime Graph and the Non-Commuting Graph of a Group[J].Advances in Pure Mathematics,2012,2(6):391-396.
4Qinhai Zhang,Libo Zhao,Miaomiao Li,Yiqun Shen.Finite p-Groups all of Whose Subgroups of Index p^(3) are Abelian[J].Communications in Mathematics and Statistics,2015,3(1):69-162. 被引量：10
5Dong Xie,Chunling Xu,Anmin Wang.Quantum metrology with coherent superposition of two different coded channels[J].Chinese Physics B,2021,30(9):111-116.
6Jiawei Liu,Yue Wang.Convergence of the Generalized Kähler-Ricci Flow[J].Communications in Mathematics and Statistics,2015,3(2):239-261.
7Juping Tang,Jia Zhang,Long Miao.New Criteria for Quasi-F-Groups[J].Communications in Mathematics and Statistics,2019,7(1):25-32. 被引量：2
8胡传峰,姬秀.两类极小谱任意符号模式矩阵[J].商丘师范学院学报,2020(12):8-11.
9DENG Aiping,GONG Xiaoyue,MA Hongcai.Linear Dynamical System over Finite Distributive Lattice[J].Journal of Donghua University(English Edition),2021,38(3):264-271. 被引量：1
10Tao Zheng,Xiuyun Guo.The Normalizer Property for Finite GroupsWhose Sylow 2-Subgroups are Abelian[J].Communications in Mathematics and Statistics,2021,9(1):87-99.

Communications in Mathematics and Statistics

2021年第2期

浏览历史

内容加载中请稍等...

A Classification of Finite Metahamiltonian p-Groups

参考文献8

二级参考文献35

共引文献19

相关作者

相关机构

相关主题

浏览历史