{"paper":{"title":"On the Faithful Projective Representations of Finite Groups and their Minimal Dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Poonam Nayak, Sumana Hatui","submitted_at":"2026-05-26T16:57:55Z","abstract_excerpt":"The first part of this article is devoted to characterizing the cocycles $\\alpha$ of a finite group $G$ that give rise to faithful projective representations of $G$. We prove that a $p$-group $G$ admits a faithful irreducible projective representation if and only if the cohomology class $[\\alpha]$ does not lie in the image of the inflation map $\\operatorname{inf}: \\mathrm{H}^2\\!\\left(G / N, \\mathbb{C}^{\\times}\\right) \\longrightarrow \\mathrm{H}^2\\!\\left(G, \\mathbb{C}^{\\times}\\right)$ for any non-trivial central subgroup $N$ of $G$. In the case where $[\\alpha] \\in \\operatorname{Im}(\\operatorname"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27280","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.27280/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}