{"paper":{"title":"Fixating Group Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Augustin Fruchard (LMIA), Bernard Brighi (LMIA), Guido Ahumada (IRIMAS), Nicolas Chevallier (IRIMAS)","submitted_at":"2019-01-25T14:52:11Z","abstract_excerpt":"A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french \"groupe {\\`a} points fixes\") if any element of G has at least one fixed point in X. The G group is said with a common fixed point (abbreviated as gag for \"groupe {\\`a} point fixe global\") if there is x $\\in$ X fixed by all elements of G. The group G is said fixating if any subgroup of G which is a gaf is automatically a gag. The article explores which groups are fixating. The situation depends on the assumptions made on the group of bijections and on the support set X. For example the group "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08895","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"}