置换性很好的一类群

Some groups with a good permutability of subgroups

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.