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无限群p拟Frattini子群
  • 期刊名称：成都信息工程学院学报, 2010, 25(2), 213-217
  • 时间：0
  • 分类：O152[理学—数学;理学—基础数学]
  • 作者机构：[1]成都信息工程学院数学学院,四川成都610225
  • 相关基金：国家自然科学基金资助项目（10771180）
  • 相关项目：群的结构及若干疑难问题研究
关键词： 基础数学, 无限群论, p拟非生成元, p拟极大子群, p拟Frattini子群, pF群, Pure mathematics, the theory of infinite groups, non-pnear generators of groups, p nearly maximal sub-groups of groups, thepnear Frattini subgroups of groups, pFgroups
中文摘要：

群G中所有极大子群之交称之为G的Frattini子群。给出一种新的广义的Frattini子群——p拟Fratti—ni子群的定义，并研究基本性质，例如p拟既约性质、p拟可消性质和p拟补充性质等。同时对正规子群，同态像和直积的p拟Frattini子群也进行了研究。

英文摘要：

The Frattini subgroup Frat （G） of a group is defined as the intersection of the maximal subgroups by G. The object of this paper is to introduee a new canonical subgroup, thepnear Frattini subgroups. Its definition is given and its properties are investigated, such as thepnear irreducibility, thepnear eliminability and thepnear supplementa- tion property. At the same time, thepnear Frattini subgroups of normal subgroups, homomorphism images and direct products of groups are also considered.

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