论文标题
在具有环状缺陷组的源代数等效类上，i
On the source algebra equivalence class of blocks with cyclic defect groups, I
论文作者
论文摘要
我们研究了有限组的循环缺陷组的P块的源代数类。通过Linckelmann的工作，该类是由块的Brauer树和其顶点上的符号函数和一个缺陷组的内部permuntion模块进行了参数。我们证明，可以从组的角色表中读取此内部渗透模块。我们还证明，对于所有具有简单商的准基团的环形组的循环p块都是微不足道的，它是一个零星的组，交替的群体，一个定义特征性的谎言类型，或在特定特征中的一组谎言类型，prime prime p prime p prime在某些意义上足够大。
We investigate the source algebra class of a p-block with cyclic defect groups of the group algebra of a finite group. By the work of Linckelmann this class is parametrized by the Brauer tree of the block together with a sign function on its vertices and an endo-permutation module of a defect group. We prove that this endo-permutation module can be read off from the character table of the group. We also prove that this module is trivial for all cyclic p-blocks of quasisimple groups with a simple quotient which is a sporadic group, an alternating group, a group of Lie type in defining characteristic, or a group of Lie type in cross-characteristic for which the prime p is large enough in a certain sense.
