摘要
设G和H是两个有限群,R是复数域C中所有代数整数构成的环。用RG表示G在R上的群代数,Z(RG)是RG的中心。在这篇注记中,设Z(RG)≌Z(RH),如果G是内幂零群,那么群H不一定是内幂零群。进一步,群H的结构也可以得到。
Let G and H be two finite groups, R is the ring of all the algebraic integers in the field C of complex numbers. Denote the group algebra of G over R by RG and the central of RG by Z（RG）. In this note, the following question is discussed： Suppose that Z（RG）≌Z（RH）, then H is not necessarily an inner nilpotent group if G is an inner nilpotent group. Furthermore, the structure of the finite group H can be obtained.
出处
《青岛大学学报（自然科学版）》
CAS
2011年第1期21-24,共4页
Journal of Qingdao University(Natural Science Edition)
基金
山东省自然基金资助项目(Y2008A03)
关键词
中心群代数
群代数
中心本原幂等元
central group algebra
group algebra
central primitive idempotent
