Blocks of Defect Zero and Products of Elements of Orderp
Blocks of Defect Zero and Products of Elements of Orderp
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DOI：
10.1006/jabr.1998.7715
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发表时间：
1999-04
影响因子：
0.9
通讯作者：
J. Murray
中科院分区：
文献类型：
--
作者：
J. Murray
摘要 假设G是一个有限群，F是一个特征域p > 0，它是G所有子群的分裂域。令te0 为FG 中缺陷零的块幂等之和，并令Ω 为G 中gp = 1 的解集。我们证明，当 p 为奇数时，e0 = (Ω + )2，当 p = 2 时，e0 = (Ω + )3。在后一种情况下 (Ω + )2 = R + ，其中 Ri 是 2-缺陷零的实数元素集合。 Soe0 = Ω + R + = (R + )2。我们还证明，当 p = 2 时，e0 = Ω + Ω + 4 = (Ω + 4)2，其中 Ω4 是 tog4 = 1 的解集。这些结果为我们提供了缺陷零 p 块存在的各种标准。
Abstract Suppose thatGis a finite group and thatFis a field of characteristicp > 0 which is a splitting field for all subgroups ofG. Lete0be the sum of the block idempotents of defect zero inFG, and let Ω be the set of solutions togp = 1 inG. We show thate0 = (Ω + )2, whenpis odd, ande0 = (Ω + )3, whenp = 2. In the latter case (Ω + )2 = R + , whereRis the set of real elements of 2-defect zero. Soe0 = Ω + R + = (R + )2. We also show thate0 = Ω + Ω + 4 = (Ω + 4)2, whenp = 2, where Ω4is the set of solutions tog4 = 1. These results give us various criteria for the existence ofp-blocks of defect zero.