{"paper":{"title":"Hopf Galois structures on separable field extensions of odd prime power degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Marta Salguero, Teresa Crespo","submitted_at":"2018-07-30T16:01:56Z","abstract_excerpt":"A Hopf Galois structure on a finite field extension $L/K$ is a pair $(\\mathcal{H},\\mu)$, where $\\mathcal{H}$ is a finite cocommutative $K$-Hopf algebra and $\\mu$ a Hopf action. In this paper, we present several results on Hopf Galois structures on odd prime power degree separable field extensions. We prove that if a separable field extension of odd prime power degree has a Hopf Galois structure of cyclic type, then it has no structure of noncyclic type. We determine the number of Hopf Galois structures of cyclic type on a separable field extension of degree $p^n$, $p$ an odd prime, such that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11409","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}