{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/classifying-primitive-solvable-permutation","title":"Classifying Primitive Solvable Permutation Groups of Rank 5 and 6","arxiv_id":"2308.13043","date":"2023-08-24","proceeding":null,"authors":["Anakin Dey","Kolton O'Neal","Duc Van Khanh Tran","Camron Upshur","Yong Yang"],"abstract":"Let $G$ be a finite solvable permutation group acting faithfully and primitively on a finite set $\\Omega$. Let $G_0$ be the stabilizer of a point $\\alpha \\in \\Omega$ The rank of $G$ is defined as the number of orbits of $G_0$ in $\\Omega$, including the trivial orbit $\\{\\alpha\\}$. In this paper, we completely classify the cases where $G$ has rank 5 and 6, continuing the previous works on classifying groups of rank 4 or lower.","url_abs":"https://arxiv.org/abs/2308.13043v2","url_pdf":"https://arxiv.org/pdf/2308.13043v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"classifying-primitive-solvable-permutation","repo_url":"https://github.com/spamakin/solvable-primitive-permutation-groups-of-rank-5-and-6","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}