Let $G$ be a finite group. A subgroup $H$ of $G$ is called an $\mathcal{H}$-subgroup in $G$ if $N_G(H)\cap H^{g}\leq H$ for all $g\in G$. A subgroup $H$ of $G$ is called a weakly $\mathcal{H}^{\ast}$-subgroup in $G$ if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is an $\mathcal{H}$-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 $\mathcal{H}^{\ast}$-subgroup in $G$. Our results improve and extend a series of recent results in the literature.
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Heliel, A., Hijazi, R., & Al-Obidy, R. (2014). Finite groups whose minimal subgroups are weakly H*-subgroups. International Journal of Group Theory, 3(3), 1-11. doi: 10.22108/ijgt.2014.3837
MLA
Abdelrahman Abdelhamid Heliel; Rola Asaad Hijazi; Reem Abdulaziz Al-Obidy. "Finite groups whose minimal subgroups are weakly H*-subgroups". International Journal of Group Theory, 3, 3, 2014, 1-11. doi: 10.22108/ijgt.2014.3837
HARVARD
Heliel, A., Hijazi, R., Al-Obidy, R. (2014). 'Finite groups whose minimal subgroups are weakly H*-subgroups', International Journal of Group Theory, 3(3), pp. 1-11. doi: 10.22108/ijgt.2014.3837
VANCOUVER
Heliel, A., Hijazi, R., Al-Obidy, R. Finite groups whose minimal subgroups are weakly H*-subgroups. International Journal of Group Theory, 2014; 3(3): 1-11. doi: 10.22108/ijgt.2014.3837
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