中心化子对群的影响

The Influence of Centralizer on Group

交换子群是群中相当重要的一类子群,它对群的结构有很大影响.通过对交换子群的中心化子的约束,本文得到了B-群的定义:称有限群G为B-群,如果对于任意交换子群A∈G,有CG(A)=G或CG(A)=AG成立,并讨论了B-群的结构及性质.

Abelian subgroup is a kind of important group. By restricted on the centralizer of abelian subgroup, there is a definition of B- group ： Call a fintie group G B- if either Cc （A） = G or CG （ A ） = A^G for any abelian subgroup A of G. The structure and nature of B- group were discussed in this paper.