| 具有中心群代数同构的两个有限群 |
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| 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. |
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| 作者姓名： | 王琰 海进科 |
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| 作者单位： | 青岛大学数学科学学院,山东,青岛,266071 |
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| 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。
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| 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 |
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| 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. |
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| Authors: | WANG Yan HAI Jin-ke |
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| Institution: | WANG Yan,HAI Jin-ke(College of Mathematics,Qingdao University,Qingdao 266071,China) |
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| 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. |
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| Keywords: | central group algebra group algebra central primitive idempotent |
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