Invariant Sylow subgroups and solvability of finite groups

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• 作者：Antonio Beltrán
• 关键词：Primary 20D20 ; Secondary 20D45 ; Coprime action ; Sylow subgroups ; Solvable groups
• 刊名：Archiv der Mathematik
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：106
• 期：2
• 页码：101-106
• 全文大小：410 KB
• 参考文献：1.M. Aschbacher, Finite group theory, Second edition. Cambridge Studies in Advanced Mathematics, 10. Cambridge University Press, Cambridge, 2000.
  2.J.H. Conway et al., Atlas of Finite Groups, Oxford University Press, Eynsham, 1985.
  3.The GAP Group, GAP - Groups, Algorithms and Programming, Vers. 4.7.7; 2015. (http://​www.​gap-system.​org )
  4.H. Kurzweil, and B. Stellmacher, The Theory of Finite Groups, An introduction, Springer-Verlag, New York, 2004.
  5.G. Navarro, Number of Sylow subgroups in p-solvable groups, Proc. Amer. Math. Soc. 131 (2003), 3019–3020 (electronic).
  6.Toborg I., Waldecker R.: Finite simple 3’-groups are cyclic or Suzuki groups. Arch. Math. (Basel) 102, 301–312 (2014)MATH MathSciNet CrossRef
  
• 作者单位：Antonio Beltrán (1)
  
  1. Departamento de Matemáticas, Universidad Jaume I, 12071, Castellón, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3. Keywords Coprime action Sylow subgroups Solvable groups