\(c^*\) -Normal and s-semipermutable subgroups in finite groups

详细信息    查看全文

• 作者：Guo Zhong ; Huayu Liu ; Guixiong Li ; Lianbi Jiang ; Junpei Luo
• 关键词：$$c^*$$ c ∗ ; Normal subgoup ; $$s$$ s ; Semipermutable subgroup ; $$p$$ p ; Nilpotent ; Saturated formation ; 20D10 ; 20D20
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：27
• 期：1-2
• 页码：115-120
• 全文大小：367 KB
• 参考文献：1.Doerk, K., Hawkes, T.: Finite Soluble Groups. Walterde Gruyter, Berlin (1992)CrossRef MATH
  2.Deskins, W.E.: On quasinormal subgroups of finite groups. Math. Z. 82, 125–132 (1963)CrossRef MathSciNet MATH
  3.Gorenstein, D.: Finite Group. Chelsea, New York (1980)
  4.Hans, K., Bernd, S.: The Theory of Finite Groups. Springer, Berlin (2004)MATH
  5.Huppert, B.: Endliche Gruppen I. Springer, Berlin (1967)CrossRef MATH
  6.Li, Y.: On \(s\) -semipermutable and \(c\) -normal subgroups of finite groups. Arab. J. Sci. Eng. Sect. A Sci. 34(2), 167–175 (2009)MathSciNet
  7.Kegel, O.: Sylow-Gruppen und Subnormalteiler endlicher Gruppen. Math. Z. 78, 205–221 (1962)CrossRef MathSciNet MATH
  8.Robinson, D.: A Course in the Theory of Groups. Springer, New York (1982)CrossRef MATH
  9.Schmidt, P.: Subgroups permutable with all Sylow subgroups. J. Algebra 207, 285–293 (1998)CrossRef MathSciNet
  10.Wang, Y.: \(c\) -normality of groups and its properties. J. Algebra 180, 954–965 (1996)CrossRef MathSciNet MATH
  11.Wei, H., Wang, Y.: On \(c^*\) -normality and its properties. J. Group Therory 10, 211–223 (2007)MATH
  12.Wei, H., Wang, Y., Li, Y.: On \(c\) -normal maximal and minimal subgroups of Sylow subgroups of finite groups II. Commun. Algebra 31(10), 4807–4816 (2003)CrossRef MathSciNet MATH
  13.Zhao, T., Li, X.: \(ss\) -Quasinormal subgroups of finite groups. J. Algebra Appl. 9(6), 977–984 (2010)CrossRef MathSciNet MATH
  14.Zhang, Q., Wang, L.: The influence of \(s\) -semipermutable subgroups on the structure of a finite group. Acta Math. Sin. 48, 81–88 (2005)MATH
  
• 作者单位：Guo Zhong (1)
  Huayu Liu (1)
  Guixiong Li (1)
  Lianbi Jiang (1)
  Junpei Luo (1)
  
  1. Jixiang Primary School, Shenzhen, 518000, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

A subgroup \(H\) of a group \(G\) is called \(c^*\)-normal in \(G\) if there exists a normal subgroup \(N\) of \(G\) such that \(G=HN\) and \(H\cap N\) is \(S\)-quasinormally embedded in \(G\). A subgroup \(K\) of \(G\) is said to be \(s\)-semipermutable if it is permutable with every Sylow \(p\)-subgroup of \(G\) with \((p, |K|)=1\). In this article, we investigate the influence of \(c^*\)-normality and \(s\)-semipermutability of subgroups on the structure of finite groups and generalize some known results. Keywords \(c^*\)-Normal subgoup \(s\)-Semipermutable subgroup \(p\)-Nilpotent Saturated formation