Principal 2-blocks and Sylow 2-subgroups: PRINCIPAL 2-BLOCKS AND SYLOW 2-SUBGROUPS
Principal 2-blocks and Sylow 2-subgroups: PRINCIPAL 2-BLOCKS AND SYLOW 2-SUBGROUPS
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Primary 2-blocks 和 Sylow 2-subgroups: PRINCIPAL 2-BLOCKS AND SYLOW 2-SUBGROUPS
DOI：
10.1112/blms.12181
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发表时间：
2018
影响因子：
0.9
通讯作者：
Taylor, Jay
中科院分区：
文献类型：
--
作者：
Schaeffer Fry, A. A.;Taylor, Jay
设是一个有限群，具有Sylow 2-子群。Navarro-Tiep-巴列霍证明了的主2-块恰好包含一个不可约Brauer特征标当且仅当的主2-块中的所有奇数次普通不可约特征标都被某个伽罗瓦自同构固定。Navarro-Vallejo最近的工作将这个猜想简化为几乎简单的群。我们发现，猜想持有的所有相关的几乎单群，从而建立猜想的所有有限群。
Letbe a finite group with Sylow 2‐subgroup. Navarro–Tiep–Vallejo have conjectured that the principal 2‐block ofcontains exactly one irreducible Brauer character if and only if all odd‐degree ordinary irreducible characters in the principal 2‐block ofare fixed by a certain Galois automorphism. Recent work of Navarro–Vallejo has reduced this conjecture to almost simple groups. We show that the conjecture holds for all relevant almost simple groups, thus establishing the conjecture for all finite groups.