A note on blocks of characters of a finite group
A note on blocks of characters of a finite group
复制标题
关于有限群字符块的注解
DOI：
10.1016/0021-8693(72)90099-3
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发表时间：
1972
影响因子：
0.9
通讯作者：
K. Iizuka
中科院分区：
文献类型：
--
作者：
K. Iizuka
设6是有限阶群，A [@]是特征为p，p为有理素数的代数闭域/l上的8的群代数，2是A [@]的中心. R. Brauer在他的论文[3]中给出了关于Q的块、缺陷群和p-截面的重要结果，这些结果与Brauer [I，21]中的结果密切相关。在文献[3]中，许多结果被写成定义在中心2上的线性函数的结果。在本注记中，我们将采用Osima [7]，Iizuka [4，51]和Iizuka-Sasaki[6]中所采用的方法来研究其中的一些结果。令R1，s1，，.，51，是6中共轭元素的类，用&表示A [@]中属于SD的所有元素的和，/3= 1，2，.，n.众所周知，K1，Kz，...，Kn形成2的a/l-基。让
Let 6 be a group of finite order and A [@] the group algebra of 8 over an algebraically closed field/l of characteristic p, p rational prime, and 2 the center of A [@]. Prof. R. Brauer, in his paper [3], has given important results concerning blocks, defect groups and p-sections of Q and closely relating to the results which were announced in Brauer [I, 21. In [3], many of the results are written as those on linear functions which are defined on the center 2. In the present note, we shall study some of the results in the way which was adopted in Osima [7], Iizuka [4, 51 and Iizuka-Sasaki[6].1. Let R,, s\,,..., 51, be the classes of conjugate elements in 6 and denote by & the sum of all elements belonging to SD in A [@],/3= 1, 2,..., n. As is well known, K1, Kz,..,, Kn form a/l-basis of 2. Let