{"paper":{"title":"On Clifford theory with Galois action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Frieder Ladisch","submitted_at":"2014-09-11T19:54:44Z","abstract_excerpt":"Let $\\widehat{G}$ be a finite group, $N $ a normal subgroup of $\\widehat{G}$ and $\\theta\\in \\operatorname{Irr}N$. Let $\\mathbb{F}$ be a subfield of the complex numbers and assume that the Galois orbit of $\\theta$ over $\\mathbb{F}$ is invariant in $\\widehat{G}$. We show that there is another triple $(\\widehat{G}_1,N_1,\\theta_1)$ of the same form, such that the character theories of $\\widehat{G}$ over $\\theta$ and of $\\widehat{G}_1$ over $\\theta_1$ are essentially \"the same\" over the field $\\mathbb{F}$ and such that the following holds: $\\widehat{G}_1$ has a cyclic normal subgroup $C$ contained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3559","kind":"arxiv","version":3},"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"}