摘要
主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B群的结构进行一些刻画.应用B群的结构得到有限p(p>2)群为二元生成的B群的充要条件.
The paper studies the influence of subgroups replacement properties on the structure of finite groups. A finite group is derived from the subgroup replacement properties, which is called B group. B groups is the extension of full permutation groups, the power of p center expansion of full permutation groups and Subgroups order use to get some properties of B groups and descriptions about the structure of B groups. By using the structure of B group, we get the necessary and sufficient conditions of a finite p (p〉 2) group being a binary generating B group.
出处
《纯粹数学与应用数学》
CSCD
2014年第5期491-495,共5页
Pure and Applied Mathematics
基金
福建省中青年教师教育科研项目(JB14108)
福建省自然科学基金(2012J01022)
关键词
有限群
B
群
有限P群
finite groups
B groups
finite p groups