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May 9, 2023 at 13:10 vote accept semisimpleton
May 8, 2023 at 8:21 history edited Dave Benson CC BY-SA 4.0
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May 8, 2023 at 8:16 comment added Dave Benson It means that the fusion systems are equivalent. See the book of Craven, "The theory of fusion systems" or the book of Aschbacher, Kessar and Oliver, "Fusion systems in algebra and topology" for the relevant notions. Roughly speaking, it means that there's an isomorphism of the Sylow subgroups that respects (elementwise) conjugacy of subgroups in the ambient group.
May 8, 2023 at 8:13 comment added semisimpleton Thanks for the answer! May I know what it means for a pair of finite groups to be "indistinguishable from the point of view of fusion" at a prime?
May 8, 2023 at 7:55 history answered Dave Benson CC BY-SA 4.0