On c -Normal Maximal and Minimal Subgroups of Sylow Subgroups of Finite Groups. II
On c -Normal Maximal and Minimal Subgroups of Sylow Subgroups of Finite Groups. II
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DOI：
10.1081/agb-120023133
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
Huaquan Wei;Yanming Wang;Yangming Li
中科院分区：
文献类型：
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作者：
Huaquan Wei;Yanming Wang;Yangming Li
G的一个子群H称为在G中c-正规的，如果存在G的一个正规子群N使得HN=G且H∩N≤HG=CORE(H)。在假设G的某个正规子群的广义拟合子群的Sylow子群的所有极大子群或极小子群在G中c-正规的条件下，我们推广了对有限群结构的研究。本文证明的主要定理是：定理设ℱ是包含𝒰的饱和群系。设G是具有正规子群H的群，使得G/H∈ℱ。如果F*(H)的任一Sylow子群的所有极大子群在G中c-正规，则G∈ℱ.定理设ℱ是包含𝒰的饱和群系。设G是具有正规子群H的群，使得G/H∈ℱ。如果F*(H)的所有极小子群和所有循环子群在G中c-正规，则G∈ℱ。
Abstract A subgroup H of G is said to be c-normal in G if there exists a normal subgroup N of G such that HN = G and H ∩ N ≤ H G = Core(H). We extend the study on the structure of a finite group under the assumption that all maximal or minimal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of G are c-normal in G. The main theorems we proved in this paper are: Theorem Let ℱ be a saturated formation containing 𝒰. Suppose that G is a group with a normal subgroup H such that G/H ∈ ℱ. If all maximal subgroups of any Sylow subgroup of F*(H) are c-normal in G, then G ∈ ℱ. Theorem Let ℱ be a saturated formation containing 𝒰. Suppose that G is a group with a normal subgroup H such that G/H ∈ ℱ. If all minimal subgroups and all cyclic subgroups of F*(H) are c-normal in G, then G ∈ ℱ.