Finite groups whose minimal subgroups are weakly H*-subgroups

Heliel, Abdelrahman Abdelhamid; Hijazi, Rola Asaad; Al-Obidy, Reem Abdulaziz

doi:10.22108/ijgt.2014.3837

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	Finite groups whose minimal subgroups are weakly H*-subgroups
International Journal of Group Theory
مقاله 1، دوره 3، شماره 3، آذر 2014، صفحه 1-11 اصل مقاله (301.12 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2014.3837
نویسندگان
Abdelrahman Abdelhamid Heliel^* ¹؛ Rola Asaad Hijazi²؛ Reem Abdulaziz Al-Obidy²
¹Department of Mathematics, Faculty of Science, Beni-Suef university
²Department of Mathematics, Faculty of Science, KAU, Saudi Arabia
چکیده
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.
کلیدواژه‌ها
‎weakly $mathcal{H}$-subgroup؛ weakly‎ ‎$mathcal{H}^{ast}$-subgroup‎؛ ‎c-supplemented subgroup‎؛ ‎generalized‎ ‎Fitting subgroup‎؛ ‎saturated formation

مراجع
M. M. Al-Shomrani, M. Ramadan and A. A. Heliel (2012) Finite groups whose minimal subgroups are weakly $\mathcal{H}$-subgroups Acta Math. Sci. Ser. B Engl. Ed. 32 (6), 2295-2301 M. Asaad, A. A. Heliel and M. M. Al-Shomrani (2012) On weakly mathcalH-subgroups of finite groups Comm. Algebra 40 (9), 3540-3550 A. Ballester-Bolinches, Y. Wang and X. Guo (2000) C -Supplemented subgroups of finite groups Glasg. Math. J. 42 (3), 383-389 M. Bianchi, A. Gillio Berta Mauri, M. Herzog and L. Verardi (2000) On finite solvable groups in which normality is a transitive relation J. Group Theory 3, 147-156 J. Buckley (1970) Finite groups whose minimal subgroups are normal Math. Z. 116, 15-17 P. Csorgo and M. Herzog (2004) On supersolvable groups and the nilpotator Comm. Algebra 32 (2), 609-620 K. Doerk and T. Hawkes (1992) Finite Soluble Groups Walter de Gruyter, Berlin-New York B. Huppert (1979) Endliche Gruppen I Springer, Berlin-New York B. Huppert and N. Blackburn (1982) Finite Groups III Springer, Berlin-New York Y. Li (2002) Some notes on the minimal subgroups of Fitting subgroups of finite groups J. Pure Appl. Algebra 171, 289-294 M. Ramadan, M. Ezzat Mohamed and A. A. Heliel (2005) On c-normality of certain subgroups of prime power order of finite groups Arch. Math. (Basel) 85, 203-210 Y. Wang (1996) C-Normality of groups and its properties J. Algebra 180, 954-965 Y. Wang, Y. Li and J. Wang (2003) Finite groups with c-supplemented minimal subgroups Algebra Colloq. 10 (3), 413-425 H. Wei (2001) On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups Comm. Algebra 29 (5), 2193-2200 H. Wei, Y. Wang and Y. Li (2003) On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups II Comm. Algebra 31 (10), 4807-4816 H. Wei, Y. Wang and Y. Li (2004) On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups Proc. Amer. Math. Soc. 132 (8), 2197-2204
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Finite groups whose minimal subgroups are weakly H*-subgroups