https://amey-thakur.github.io/tags/transitive-groups/Recent content in Transitive Groups on AmeyArcHugo -- 0.152.2en-usSun, 20 Sep 2026 09:00:00 -0400https://amey-thakur.github.io/posts/2026-09-20-chebotarev-fingerprints-identifying-degree-24-galois-groups/Sun, 20 Sep 2026 09:00:00 -0400https://amey-thakur.github.io/posts/2026-09-20-chebotarev-fingerprints-identifying-degree-24-galois-groups/Naming the Galois group of a degree-24 integer polynomial ordinarily demands resolvent computations inside a computer algebra system. This paper presents a statistical alternative that needs only polynomial factorisation modulo small primes, and evaluates it against 576,682 polynomials whose groups the SAIR IGP24 evaluation server computed independently in Magma. The method reads the multiset of Frobenius cycle types at 60 primes as a sample from the group’s own cycle-type distribution, which the Chebotarev density theorem licenses, then scores that sample against empirical profiles of candidate groups drawn by product-replacement sampling. Within its domain the classifier reaches 69.0% top-1 and 88.7% top-3 accuracy at 53 ms per polynomial.