数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2295-2301.doi: 10.1016/S0252-9602(12)60179-9

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FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

M. M. Al-Mosa Al-Shomrani|M. Ramadan|A. A. Heliel   

  1. 1.Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia; 2.Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt; 3.Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia Department of Mathematics, Beni-Suef University, Faculty of Science 62511, Beni-Suef, Egypt
  • 收稿日期:2011-06-09 修回日期:2012-03-21 出版日期:2012-11-20 发布日期:2012-11-20
  • 基金资助:

    The research supported by the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) represented by the Unit of Research Groups through the grant number (MG/31/01) for the group entitled “Abstract Algebra and its Applications”.

FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

M. M. Al-Mosa Al-Shomrani|M. Ramadan|A. A. Heliel   

  1. 1.Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia; 2.Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt; 3.Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia Department of Mathematics, Beni-Suef University, Faculty of Science 62511, Beni-Suef, Egypt
  • Received:2011-06-09 Revised:2012-03-21 Online:2012-11-20 Published:2012-11-20
  • Supported by:

    The research supported by the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) represented by the Unit of Research Groups through the grant number (MG/31/01) for the group entitled “Abstract Algebra and its Applications”.

摘要:

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hg ≤ H for all g ∈ G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and HK is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.

关键词: c-normal subgroup, H-subgroup, p-nilpotent group, supersolvable group, generalized Fitting subgroup, saturated formation

Abstract:

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hg ≤ H for all g ∈ G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and HK is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.

Key words: c-normal subgroup, H-subgroup, p-nilpotent group, supersolvable group, generalized Fitting subgroup, saturated formation

中图分类号: 

  • 20D10