The McKay conjecture and Galois automorphisms
The McKay conjecture and Galois automorphisms
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DOI：
10.4007/annals.2004.160.1129
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发表时间：
2004-11
影响因子：
4.9
通讯作者：
G. Navarro
中科院分区：
文献类型：
--
作者：
G. Navarro
有限群表示论的主要问题是寻找有限群G的某些全局不变量可以局部计算的若干猜想的证明。这些猜想中最简单的是？麦凯猜想?在G的p- sylow归一化式化中，我们提出了这个猜想的一个更强的版本，它处理了伽罗瓦自同构。事实上，同样的想法也适用于著名的Alperin和Dade猜想。
The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ?McKay conjecture? which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.