Brauer第24问题的推广

A Generalization of Brauer’s Problem 24

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．

In this note we use the theory of blocks with cyclic defect groups to extend the study on Brauer’s problem 24(see ). We prove the following theorem: Let G be a finite group with a cyclic Sylow p-subgroup P. Assume |P|=p a, where a is a positive integer. Let P i be the unique subgroup of order p i of P,1ia. Then |Cl(G)|=|Cl(N G(P i)| if and only if P iG.