Finite groups with generalized subnormal embedding of Sylow subgroups

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• 作者：A. F. Vasil’ev ; T. I. Vasil’eva ; A. S. Vegera
• 刊名：Siberian Mathematical Journal
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：57
• 期：2
• 页码：200-212
• 全文大小：267 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260
• 卷排序：57

文摘

Given a set π of primes and a hereditary saturated formation F, we study the properties of the class of groups G for which the identity subgroup and all Sylow p-subgroups are F-subnormal (K-F-subnormal) in G for each p in π. We show that such a class is a hereditary saturated formation and find its maximal inner local screen. Some criteria are obtained for the membership of a group in a hereditary saturated formation in terms of its formation subnormal Sylow subgroups.Keywordsfinite groupSylow subgroupformationhereditary saturated formationF-subnormal subgroupK-F-subnormal subgrouplocal screen