{"id":"openai-math/Cyclic-Length-and-Chromatic-Fixed-Point-Loss","pdf":"https://github.com/openai/math/blob/main/preprints/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026","tags":["finite-groups","chromatic-homotopy","group-theory"],"score":0,"title":"Cyclic length and chromatic fixed-point loss","domain":"Topology","family":"314","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"For a finite p -group G and a subgroup H , we prove that the optimal chromatic fixed-point loss equals the shortest length of a subnormal chain from H to G with cyclic quotients. The equality holds at every prime and every nonnegative height, resolving positively the equality proposed by Kuhn and Lloyd.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Cyclic length and chromatic fixed-point loss"}