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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.06471 |
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Table of Contents:
- The Glauberman correspondence and its generalisation, the Dade--Glauberman--Nagao (DGN) correspondence, play an important role in studying local-global counting conjectures and their reductions to (quasi-)simple groups. These reduction theorems require an additional set of compatibility conditions for the DGN correspondence. In this paper, we prove that there exists a bijection of irreducible Brauer characters above the DGN correspondence that is equivariant with Galois automorphisms and group automorphisms and preserves vertices. Our proof utilizes the framework of $\hH$-triples developed by Navarro--Späth--Vallejo. The results establish a reduction theorem for the Galois Alperin weight conjecture.