FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

doi:10.1016/S0252-9602(12)60179-9

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

FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

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

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.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/Abstract

摘要：

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if N_G(H)∩H^g ≤ 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 H∩K 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:

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

中图分类号:

20D10

M. M. Al-Mosa Al-Shomrani, M. Ramadan, A. A. Heliel. FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS[J]. 数学物理学报(英文版), 2012, 32(6): 2295-2301.

M. M. Al-Mosa Al-Shomrani, M. Ramadan, A. A. Heliel. FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2295-2301.

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FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

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