FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS  

作　　者：M.M.Al-Mosa Al-Shomrani M.Ramadan A.A.Heliel 

机构地区：[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,Beni-Suef University,Faculty of Science 62511,Beni-Suef,Egypt

出　　处：《Acta Mathematica Scientia》2012年第6期2295-2301,共7页数学物理学报（B辑英文版）

基　　金：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）∩ H^g ≤ H for all g C 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 N 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.Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C 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 N 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 subgroupi saturated formation 

分 类 号：O152.1[理学—数学]