On $c$-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups
نویسندگان
چکیده
منابع مشابه
ON c-SUPPLEMENTED MAXIMAL AND MINIMAL SUBGROUPS OF SYLOW SUBGROUPS OF FINITE GROUPS
This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .
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A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-04-07296-x