{"paper":{"title":"On Groups of Linear Fractional Transformations Stabilizing Finite Sets of Four Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Patrick Nyadjo Fonga","submitted_at":"2025-05-31T22:04:58Z","abstract_excerpt":"Let $E$ be a subset of the projective line over a commutative field $\\mathbb{K}$. When $\\mathbb{K}$ has infinite cardinality, it is well known that if $E$ contains at most three elements, then the group of linear fractional transformations preserving $E$ is either infinite or isomorphic to the symmetric group on three elements. In this work, we investigate the case where $E$ consists of four elements. We show that the group of projective linear transformations stabilizing $E$ is, depending on the characteristic of the field $\\mathbb{K}$, isomorphic to either the Klein four-group $V_4$, the dih"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00729","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/2506.00729/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"}