On nearly S-permutably embedded subgroups of finite groups

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• 作者：Kh. A. Al-Sharo (1) sharo_kh@yahoo.com
• 关键词：nearly S ; permutably embedded subgroup &#8211 ; saturated formation &#8211 ; solvable group &#8211 ; supersolvable group &#8211 ; maximal subgroup
• 刊名：Mathematical Notes
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：91
• 期：3-4
• 页码：470-478
• 全文大小：547.3 KB
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• 作者单位：1. Al-Bayt University, Mafraq, Jordan
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

Let Gbe a finite group. A subgroup H of G is said to be S-permutable in G if HP = PH for all Sylow subgroups P of G. A subgroup A of a group G is said to be S-permutably embedded in G if for each Sylow subgroup of A is also a Sylow of some S-permutable subgroup of G. In this paper, we analyze the following generalization of this concept. Let H be a subgroup of a group G. Then we say that H is nearly S-permutably embedded in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C. We study the structure of G under the assumption that some subgroups of G are nearly S-permutably embedded in G. Some known results are generalized.