Remarks on Representations of Finite Groups over an Arbitrary Field of Characteristic Zero
Remarks on Representations of Finite Groups over an Arbitrary Field of Characteristic Zero作者机构：College of Mathematics Qingdao University Shandong 266071 P. R: China
出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)
年 卷 期：2011年第31卷第3期
页 面：437-442页
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：Supported by the National Natural Science Foundation of China (Grant No.10771132) the Natural Science Foundation of Shandong Province (Grant No.Y2008A03)
主 题：ΓK-action ΓK-classes orthogonality relations.
摘 要：Let G be a finite group and K a field of characteristic *** is well-known that if K is a splitting field for G,then G is abelian if and only if any irreducible representation of G has degree *** this paper,we generalize this result to the case that K is an arbitrary field of characteristic zero（that is,K need not be a splitting field for G）,and we also obtain the orthogonality relations of irreducible K-characters of G in this *** results generalize some well-known theorems.
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