Acta mathematica scientia, Series B >
FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS
Received date: 2011-06-09
Revised date: 2012-03-21
Online 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”.
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 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.
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 . DOI: 10.1016/S0252-9602(12)60179-9
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