| 具有中心群代数同构的两个有限群 |
| |
| 引用本文： | 王琰,海进科. 具有中心群代数同构的两个有限群[J]. 青岛大学学报(自然科学版), 2011, 24(1): 21-24. DOI: 10.3969/j.issn.1006-1037.2011.01.006 |
| |
| 作者姓名： | 王琰 海进科 |
| |
| 作者单位： | 青岛大学数学科学学院,山东,青岛,266071 |
| |
| 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）丝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。
|
| 关 键 词： | 中心群代数 群代数 中心本原幂等元 |
On Finite Groups with Isomorphic Centers of Group Rings |
| |
| WANG Yan,HAI Jin-ke. On Finite Groups with Isomorphic Centers of Group Rings[J]. Journal of Qingdao University(Natural Science Edition), 2011, 24(1): 21-24. DOI: 10.3969/j.issn.1006-1037.2011.01.006 |
| |
| Authors: | WANG Yan HAI Jin-ke |
| |
| Affiliation: | WANG Yan,HAI Jin-ke(College of Mathematics,Qingdao University,Qingdao 266071,China) |
| |
| Abstract: | 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. |
| |
| Keywords: | central group algebra group algebra central primitive idempotent |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
