AI 中文总结
本文提出计算框架，验证零星群及其泛覆盖上Giannelli-McKay细化猜想，通过严格条件（等变性、导子保持、中心特征相容）及理论约简，利用Clifford理论和特征表构造不增加特征度的双射。
AI 中文摘要
我们提出一个计算框架，用于验证由E. Giannelli提出的McKay猜想的一个细化版本，该版本适用于零星单群及其泛覆盖群。此细化断言有限群的$p'$-特征与其Sylow $p$-子群正规化子的$p'$-特征之间存在一个不增加特征度的双射。我们的验证强制执行更严格的条件，确保在相关外自同构群作用下的等变性、特征导子的$p$-部分的保持以及与中心特征的相容性。我们建立了理论约简，将相关外自同构作用限制为至多2阶，从而利用Clifford理论和预计算的特征表来避免昂贵的显式群构造。最后，我们提供用于分类特征和构造严格满足这些条件的双射的算法。
英文摘要
We present a computational framework to verify a refinement of the McKay conjecture, proposed by E. Giannelli, for sporadic simple groups and their universal covers. This refinement asserts the existence of a bijection between the $p'$-characters of a finite group and those of the normalizer of its Sylow $p$-subgroup that does not increase character degrees. Our verification enforces stricter conditions, ensuring equivariance under the relevant outer automorphism group, preservation of the $p$-part of the character conductor, and compatibility with central characters. We establish theoretical reductions that limit the relevant outer automorphism action to an order of at most 2, allowing us to leverage Clifford theory and precomputed character tables to circumvent expensive explicit group constructions. Finally, we provide algorithms for classifying characters and constructing bijections that strictly satisfy these conditions.
Comments24 pages. GAP implementation included
