1. On ℱ-Quasinormal Primary Subgroups of Finite Groups.
- Author
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Miao, Long and Li, Baojun
- Subjects
FINITE groups ,QUASIGROUPS ,MATHEMATICAL proofs ,SYLOW subgroups ,GROUP theory ,G-structures ,ALGEBRAIC geometry ,MATHEMATICAL analysis - Abstract
Let G be a finite group and ℱ a formation. A subgroup H is called ℱ-quasinormal in G if there exists a quasinormal subgroup T of G such that HT is quasinormal in G and (H ∩ T)H G /H G is contained in the ℱ-hypercenter of G/H G . In this article, we study the structure of finite groups by using ℱ-quasinormal subgroups and prove that: Let ℱ be a saturated formation containing 𝒰 and G be a group with a normal subgroup H such that G/H ∈ ℱ. If every maximal subgroup of every noncyclic Sylow subgroup of F*(H) having no supersolvable supplement in G is 𝒰-quasinormal in G, then G ∈ ℱ. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
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