A splitting theorem for blocks
A splitting theorem for blocks
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DOI：
10.18910/10344
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发表时间：
1996-06
影响因子：
0.4
通讯作者：
Shigeo Koshitani;B. Külshammer
中科院分区：
文献类型：
--
作者：
Shigeo Koshitani;B. Külshammer
设F是素数特征为p的代数闭域，G是有限群，H是G的正规子群，使得G/H是^-群。此外，设B是H在F上的群代数FH的块，根据Osima定理，存在覆盖B的FG的唯一块A。我们对A的结构感兴趣，通常将一般情况归结为B是(/-稳定的)的特殊情况。因此，我们在下文中假设B是G-稳定的，用P表示A的一个亏群，则Q-Pr\H是B的一个亏群，且G=F//(见[3，V])。如果P是交换的，则A的特征标理论在R.Knόrr[5]的一篇论文中得到了描述。我们感兴趣的是，在Q在P中有补的附加假设下，A作为环的结构。我们证明了这种缺陷组的分裂意味着块的分裂：
Let F be an algebraically closed field of prime characteristic p, let G be a finite group, and let H be a normal subgroup of G such that G/H is a ^-group. Moreover, let B be a block of the group algebra FH of H over F. By Osima's theorem, there is a unique block A of FG covering B. We are interested in the structure of A. As usual, the general case reduces to the special one where B is (/-stable. Thus we assume in the following that B is G-stable and denote by P a defect group of A. Then Q\—Pr\H is a defect group of B, and G = F//(see [3, V]). If P is abelian then the character theory of A is described in a paper by R. Knόrr [5]. We are interested in the structure of A as a ring under the additional hypothesis that Q has a complement in P. We prove that such a splitting of defect groups implies a splitting of blocks: