{"paper":{"title":"$p$-Biset Functor of Monomial Burnside Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.RT","authors_text":"\\.Ibrahim Kaan Aslan, Olcay Co\\c{s}kun","submitted_at":"2025-05-21T06:11:55Z","abstract_excerpt":"We investigate the structure of the monomial Burnside biset functor over a field of characteristic zero, with particular focus on its restriction kernels. For each finite \\( p \\)-group \\( G \\), we give an explicit description of the restriction kernel at \\( G \\), and determine the complete list of composition factors of the functor. We prove that these composition factors have minimal groups \\( H \\) isomorphic either to a cyclic \\( p \\)-group or to a direct product of such a group with a cyclic group of order \\( p \\). Furthermore, we identify the simple \\( \\mathbb{C}[\\Aut(H)] \\)-modules that a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15150","kind":"arxiv","version":2},"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/2505.15150/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"}