| 符渠雷.超聚焦子群是 16 阶初等交换群的块[J].数学年刊A辑,2022,43(1):95~102 |
| 超聚焦子群是 16 阶初等交换群的块 |
| Blocks with Elementary Abelian Hyperfocal Subgroups of Order 16 |
| Received:September 04, 2020 Revised:September 03, 2021 |
| DOI：10.16205/j.cnki.cama.2022.0006 |
| 中文关键词: 有限群, 块, 超聚焦子群, 特征标 |
| 英文关键词:Finite group, Block, Hyperfocal subgroup, Character |
| 基金项目: |
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| 中文摘要: |
| 假设有限群上的块 b 被其亏群的正规化子控制, 其超聚焦子群是 16 阶的初等交换群并且包含在 亏群的中心里. 本文计算了部分情况下块 b 的不可约模特征标和不可约常特征标个数. 在这些情况下, Alperin 重量猜想是对的. |
| 英文摘要: |
| The author assumes that a block b of a ?nite group is controlled by the normalizer of its defect group, and that its hyperfocal subgroup is the elementary abelian group of order 16 and is contained in the center of the defect group. He calculates the numbers of irreducible Brauer characters and irreducible ordinary characters in this block in some cases. In these cases, the Alperin weight conjecture holds. |
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