{"paper":{"title":"A characterisation of weakly locally projective amalgams related to $A_{16}$ and the sporadic simple groups $M_{24}$ and $He$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"A. A. Ivanov, Cheryl E. Praeger, Luke Morgan, Michael Giudici","submitted_at":"2014-05-14T09:02:34Z","abstract_excerpt":"A simple undirected graph is weakly $G$-locally projective, for a group of automorphisms $G$, if for each vertex $x$, the stabiliser $G(x)$ induces on the set of vertices adjacent to $x$ a doubly transitive action with socle the projective group $L_{n_x}(q_x)$ for an integer $n_x$ and a prime power $q_x$. It is $G$-locally projective if in addition $G$ is vertex transitive. A theorem of Trofimov reduces the classification of the $G$-locally projective graphs to the case where the distance factors are as in one of the known examples. Although an analogue of Trofimov's result is not yet availabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3416","kind":"arxiv","version":3},"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"}