Finite groups with some maximal subgroups of Sylow subgroups ℳ-supplemented

被引：0
作者：
Long Miao
机构：
[1] Yangzhou University,
来源：
Mathematical Notes | 2009年 / 86卷
关键词：
Sylow subgroup; ℳ-supplemented subgroup; formation; finite group; supersolvable group; Hall subgroup; Fitting subgroup; p-nilpotent group;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A subgroup H of a group G is said to be ℳ-supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H. In this paper, we obtain the following statement: Let ℱ be a saturated formation containing all supersolvable groups and H be a normal subgroup of G such that G/H ε ℱ. Suppose that every maximal subgroup of a noncyclic Sylow subgroup of F*(H), having no supersolvable supplement in G, is ℳ-supplemented in G. Then G ε ℱ.
引用
收藏
页码：655 / 664
页数：9
相关论文
共 12 条
  • [1] Srinivasan S.(1980)Two sufficient conditions for supersolvability of finite groups Israel J. Math. 35 210-214
  • [2] Asaad M.(1991)Influence of Arch.Math. (Basel) 56 521-527
  • [3] Ramadan M.(1998)-quasinormality on maximal subgroups of Sylow subgroups of the Fitting subgroup of a finite group Comm. Algebra 26 3647-3652
  • [4] Shaalan A.(2000)On maximal subgroups of Sylow subgroups of finite groups J. Algebra 224 467-478
  • [5] Asaad M.(2005)Finite groups with some subgroups of Sylow subgroups Comm. Algebra 33 2789-2800
  • [6] Wang Y.(1987)-supplemented Bull. London Math. Soc. 19 311-319
  • [7] Miao L.(2002)Finite groups with some primary subgroups ℱ-s-supplemented Bull. Austral. Math. Soc. 65 467-475
  • [8] Guo W.(undefined)Conjugacy of odd order Hall subgroups undefined undefined undefined-undefined
  • [9] Gross F.(undefined)A generalisation of Kramer’s theorem and its applications undefined undefined undefined-undefined
  • [10] Wang Y.(undefined)undefined undefined undefined undefined-undefined
12