{"paper":{"title":"Projective linear groups as automorphism groups of chiral polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Dimitri Leemans, Eugenia O'Reilly-Regueiro, J\\'er\\'emie Moerenhout","submitted_at":"2016-06-26T09:46:40Z","abstract_excerpt":"It is already known that the automorphism group of a chiral polyhedron is never isomorphic to $PSL(2,q)$ or $PGL(2,q)$ for any prime power $q$. In this paper, we show that $PSL(2,q)$ and $PGL(2,q)$ are never automorphism groups of chiral polytopes of rank at least $5$. Moreover, we show that $PGL(2,q)$ is the automorphism group of at least one chiral polytope of rank $4$ for every $q\\geq5$. Finally, we determine for which values of $q$ the group $PSL(2,q)$ is the automorphism group of a chiral polytope of rank $4$, except when $q=p^d\\equiv3\\pmod{4}$ where $d>1$ is not a prime power, in which c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08017","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"}