{"paper":{"title":"Determining Aschbacher classes using characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Sebastian Jambor","submitted_at":"2014-02-26T02:20:41Z","abstract_excerpt":"Let $\\Delta\\colon G \\to \\mathrm{GL}(n, K)$ be an absolutely irreducible representation of an arbitrary group $G$ over an arbitrary field $K$; let $\\chi\\colon G \\to K\\colon g \\mapsto \\mathrm{tr}(\\Delta(g))$ be its character. In this paper, we assume knowledge of $\\chi$ only, and study which properties of $\\Delta$ can be inferred. We prove criteria to decide whether $\\Delta$ preserves a form, is realizable over a subfield, or acts imprimitively on $K^{n \\times 1}$. If $K$ is finite, this allows us to decide whether the image of $\\Delta$ belongs to certain Aschbacher classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6395","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"}