具有小中心商的有限p-群
On the Finite p-Group with a Small Central Quotient
DOI: 10.12677/PM.2017.74039, PDF, HTML, XML, 下载: 1,616  浏览: 3,193 
作者: 伍 星, 马玉龙, 刘海林*：云南大学数学与统计学院，云南 昆明
关键词: 有限p-群；LA-群；自同构群；Finite p-Group； LA-Group； Automorphism Group
摘要: 假设G是一个有限非交换p-群，并且G的阶大于p2 ，如果|G| 整除|Aut(G)| ，那么称G为LA-群。本文考虑了二元生成的有限p-群 ，并且满足|G:Z(G)| =p5，其中素数p≥7 。我们证明了这样的有限p-群是LA-群。
Abstract: Let G be a finite noncyclic p-group of order greater than p2 . If |G| divides |Aut(G)| , then G is called a LA-group. The purpose of this paper was to consider the class of p-group such that |G:Z(G)| =p5 with the prime p≥7 . We showed that such group G is LA-group.
文章引用：伍星, 马玉龙, 刘海林. 具有小中心商的有限p-群[J]. 理论数学, 2017, 7(4): 297-300. https://doi.org/10.12677/PM.2017.74039

参考文献

[1] Otto, A. (1966) Central Automorphisms of a Finite P-Group. Duke Math, 125, 280-287.
[2] Davitt, R.M. (1972) The Automorphism Group of Finite P-Abelian P-Groups Ill. Journal of Mathematics, 16, 76-85.
[3] Davitt, R.M. (1970) The Automorphism Group of a Finite Metacyclic P-Group. Proceedings of the American Mathematical Society, 25, 876-879.
https://doi.org/10.2307/2036770
[4] Exarchakos, T. (1989) On P-Group of Small Order. Publications de l'Institut Mathématique, 45, 73-76.
[5] Gavioli, N. (1993) The Number of Automorphisms of Groups of Order p^7. Proceedings of the Royal Irish Academy Section, A2, 177-184.
[6] Flynm, J., Machale, D. and O'Brien, E.A. (1994) Finite Groups Whose Automorphism Groups Are 2-Group. Proceedings of the Royal Irish Academy Section, A2, 137-145.
[7] Davitt, R.M. and Otto, A. (1972) On the Automorphism Group of a Finite Modular P-Group. Proceedings of the American Mathematical Society, 35, 399-404.
[8] Fouladi, S., Jamali, A.R. and Orfi, R. (2008) On the Automorphism Group of a Finite P-Group with Cyclic Frattinisubgroup. Proceedings of the Royal Irish Academy, 108 A2, 165-175.
[9] Xiao, C.C. (1990) A Conjecture on the Automorphism Group of a Finite P-Group. Rendiconti del Circolo Matematico di Palermo, 2, 347-351.
[10] Yadav, M.K. (2007) On Automorphisms of Finite P-Groups. Journal of Group Theory, 10, 859-866.
https://doi.org/10.1515/jgt.2007.064
[11] Davitt, R.M. (1980) On the Automorphism Group of a Finite P-Group with a Small Central Quotient. Canadian Mathematical Society, 5, 1168-1176.
https://doi.org/10.4153/CJM-1980-088-3
[12] Fouladi, S., Jamali, A.R. and Orfi, R. (2007) Automorphism Groups of Finite P-Groups of Co-Class 2. Journal of Group Theory, 10, 437-440.
https://doi.org/10.1515/jgt.2007.036
[13] Malinowska, I. (2001) Finite P-Groups with Few P-Automorphisms. Journal of Group Theory, 4, 395-400.
https://doi.org/10.1515/jgth.2001.029
[14] Attar, M.S. (2015) On Equality of Order of a Finite P-Group and Order of Its Automorphism Group. Bulletin of the Malaysian Mathematical Sciences Society, 38, 461-466.
https://doi.org/10.1007/s40840-014-0030-z
[15] Davitt, R.M. and Otto, A.D. (1971) On the Automorphism Group of a Finite P-Group with the Central Quotient Metacyclic. Proceedings of the American Mathematical Society, 30, 467-472.
https://doi.org/10.2307/2037717
[16] Faudree, R. (1968) A Note on the Automorphism Group of a Group. Proceedings of the American Mathematical Society, 19, 1379-1382.
[17] Huppert, B. and Endliche Gruppen, I. (1967) Die Grundlehren der math. Wissenschaften, Band 134. Springer-Verlag, Berlin and New York.

为你推荐