华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (1): 108-110.

• 应用数学与基础数学 • 上一篇    下一篇

弱 emphc-supplement 与一类群系

刘晓蕾   

  1. 山西财经大学 应用数学学院, 太原030006
  • 收稿日期:2008-12-26 修回日期:2009-03-20 出版日期:2010-01-25 发布日期:2010-01-25
  • 通讯作者: 刘晓蕾

On weak emphc-supplement and formations (Chinese)

LIU Xiao-lei   

  1. Department of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
  • Received:2008-12-26 Revised:2009-03-20 Online:2010-01-25 Published:2010-01-25
  • Contact: LIU Xiao-lei

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摘要： 利用弱 c-supplement 的概念,研究了一有限群属于一个包含超可解群类的饱和群系的 可能性, 证明了: 设 mathcalF 是一个饱和群系, 且包含 超可解群类. 再假设 N 是 G 的一个正规子群, 使得 G/NinmathcalF. 如果 对每一个 pinpi(N), 对 N 的任一个 Sylow p-子群 P, P 的每一个极大子群在 G 中是弱 c-supplement 的, 那么, Gin mathcalF.推广了某些结果.

关键词: 有限群, 弱c-supplement, 饱和群系, 有限群, 弱c-supplement, 饱和群系

Abstract: By weak c-supplement we investigated the possibility that a finite group is in a saturated formation containing all supersoluble groups. It was showed that for a saturated formation mathcalF containing all supersoluble groups, if there exists a group G such that G contins a normal subgroup N and G/N is supersoluble and if maximal subgroups of Sylow subgroups of N are c-supplemented in G, then Gin mathcalF. Some results are extended.

Key words: weak c-supplement, saturated formation, finite group, weak c-supplement, saturated formation

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