期刊文献+

有限核(2)-群

Finite Core(2)-groups
原文传递
导出
摘要 一个群G被称为核(m)-群当且仅当对G的任意子群H,︱H∶H_G︱至多可以表示成m个素数的乘积。证明了如果有限群G是核(m)-群,那么G是可解群,且G的Fitting子群在G中的指数至多是5个素数的乘积。进一步证明了如果有限超可解群G是有限核(2)-群,且群G存在极小正规子群N是阶为p3的初等交换子群,那么则存在素数p,q,使得G有交换正规子群A满足︱G∶A︱|2pq,并且G至多只有4个互不同构的西洛子群不正规。 A group Gis called a core(m)-group if and only if│H ∶HG │is a product of at most m prime numbers for each subgroup H ≤G.In this paper,it is proved that the index of the Fitting subgroup in anite core(2)-group Gisa product of at most5 prime numbers.Furthermore,it is also proved that if a supersoluble group Gis a finite core(2)-group which has a minimal normal subgroup N of order p^3,then there exist prime numbers p,q such that│G∶A││2pq for a normal abelian subgroup Aof Gand G has at most four non-isomorphic Slyow subgroups which are not normal.
作者 薛海波 吕恒
出处 《重庆师范大学学报(自然科学版)》 CAS CSCD 北大核心 2016年第6期69-71,共3页 Journal of Chongqing Normal University:Natural Science
基金 国家自然科学基金(No.11271301 No.11471226)
关键词 核(m)-群 可解群 FITTING子群 core(m)-groups solvable groups Fitting subgroups
  • 相关文献

参考文献1

二级参考文献7

  • 1徐明曜,曲海鹏.有限P群[M].北京:北京大学出版社,2010.
  • 2Buckley J T, Lennox J C, Neumann B H, Smith H and Wiegold J. Groups with all subgroups normal-by-finite[J]. J Algebra, 1995(95): 384-398.
  • 3Lennox J C, Smith H and Wiegold J. Finite p -groups in which subgroups have large cores[J]. Proceedings of the International Conference, de Gruyter, Berlin, 1996, 163-169.
  • 4Cutolo G, Khukhro E I, Lennox J C, Rinauro S, Smith H and Wiegold J. Locally finite groups all of whose subgroups boundedly finite over their cores[J]. Bull London Math Soc, 1997(29): 563-570.
  • 5Cutolo G, Khukhro E I, Lennox J C, Wiegold J, Riflauro S and Smith H. Finite core- p p -groups[J]. J Algebra, 1997(188): 701-719.
  • 6Cutolo G, Smith H and Wiegold J. On core-2 groups[J]. J Algebra, 2001(237): 813-841.
  • 7Berkovich Y and Janko Z. Structure of finite p-groups with given subgroups[J]. Contemporary Math, 2006(402): 13-93.

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部