Author/Authors :
هليل، عبدالرحمان عبدالحميد نويسنده Department of Mathematics, King Abdulaziz University, Faculty of Science 80203, Jeddah 21589, Jeddah, Saudi Arabia Heliel , Abdelrahman Abdelhamid , اسعد حجازي، رولا نويسنده Department of Mathematics, King Abdulaziz University, Faculty of Science 80203, Jeddah 21589, Jeddah, Saudi Arabia Asaad Hijazi, Rola , آل- عبيدي، ريم عبدالعزيز نويسنده Department of Mathematics, King Abdulaziz University, Faculty of Science 80203, Jeddah 21589, Jeddah, Saudi Arabia Al-Obidy, Reem Abdulaziz
Abstract :
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 subgroup K of G such that G=HK and H?K is an H-subgroup in G. We investigate the structure of the finite group G under the assumption that every cyclic subgroup of G of prime order p or of order 4 (if p=2) is a weakly H^{?}-subgroup in G. Our results improve and extend a series of recent results in the literature.
