Alperin-McKay-Navarro 猜想的一个约化定理
A Reduction Theorem for the Alperin-McKay-Navarro Conjecture
- School of Mathematics and Statistics, Central China Normal University（华中师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过将 Alperin-McKay-Navarro 猜想约化到非阿贝尔有限单群的万有覆盖群上的归纳条件，并验证若干零星群和 Suzuki 群、小 Ree 群的情形，证明了该猜想在这些情形下成立。
AI中文摘要：
我们将 Alperin-McKay-Navarro 猜想约化到非阿贝尔有限单群的万有覆盖群上的一个归纳条件。该约化产生了与 Brauer 对应相容的零高度特征双射，以及任意有限环境群中 H-三元组之间的块关系。我们记录了由此产生的算术和结构推论，包括 $p$-有理级别的保持和 Sylow 子群的特征理论准则。证明结合了半线性中心化和通过拟单分量传递，以及对中心指标的归纳。它使用了块关系的 Clifford 和粘合定理，以及两篇相关论文中建立的中心亏量 Dade-Glauberman-Nagao 对应。我们还验证了若干零星群在 Sylow 子群具有素数阶的素数处的归纳条件，并在定义特征下验证了 Suzuki 群 ${}^{2}B_{2}(2^{2m+1})$（$m \geq 2$）和小 Ree 群 ${}^{2}G_{2}(3^{2m+1})$（$m \geq 1$）。
英文摘要：
We reduce the Alperin-McKay-Navarro conjecture to an inductive condition on the universal covering groups of non-abelian finite simple groups. The reduction yields height-zero character bijections compatible with Brauer correspondence and block relations between H-triples for arbitrary finite ambient groups. We record the resulting arithmetic and structural consequences, including preservation of $p$-rationality levels and character-theoretic criteria for Sylow subgroups. The proof combines semilinear centralization and transfer through quasisimple components with induction on the central index. It uses the Clifford and gluing theorems for block relations and a central-defect Dade-Glauberman-Nagao correspondence established in two related papers. We also verify the inductive condition for several sporadic groups at primes for which the Sylow subgroups have prime order, and in defining characteristic for the Suzuki groups ${}^{2}B_{2}(2^{2m+1})$ with $m \geq 2$ and the small Ree groups ${}^{2}G_{2}(3^{2m+1})$ with $m \geq 1$.
