{"id":"W2158275659","doi":"10.1112/s0024610705022441","title":"A NEW NOTION OF TRANSITIVITY FOR GROUPS AND SETS OF PERMUTATIONS","year":2006,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Waterloo; Natural Sciences and Engineering Research Council of Canada; Mitacs; National Science Foundation","keywords":"Permutation group; Transitive relation; Combinatorics; Mathematics; Association scheme; Partition (number theory); Symmetric group; Permutation (music); Group (periodic table); Primitive permutation group; Homogeneous; Integer (computer science); Alternating group; Discrete mathematics; Cyclic permutation; Computer science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002196396,0.001020914,0.0008767474,0.003502849,0.002929674,0.005422192,0.001459124,0.001370823,0.007113591],"category_scores_gemma":[0.003442385,0.0007993761,0.002220464,0.002697002,0.007604736,0.01206273,0.004035784,0.003791954,0.001397605],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002132601,"about_ca_system_score_gemma":0.0009807864,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006745373,"about_ca_topic_score_gemma":0.0005528015,"domain_scores_codex":[0.9971216,0.0007068142,0.0002727199,0.0009469948,0.0005452981,0.0004065924],"domain_scores_gemma":[0.9971688,0.0009440666,0.0003870449,0.000762084,0.000332188,0.0004057668],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001978369,0.00001043251,0.0001408004,0.00002252282,0.000006848793,0.00007235378,0.0004285831,0.0003229306,0.0008807176,0.9942408,0.0004846595,0.003369656],"study_design_scores_gemma":[0.00002021256,0.00007538933,0.00024602,0.00003074621,0.00001666755,0.0003332055,0.000260526,0.002667209,0.000998048,0.9612266,0.03410556,0.00001984806],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1589085,0.002723005,0.664506,0.003124663,0.001640949,0.0003107683,0.00161966,0.0008046525,0.1663617],"genre_scores_gemma":[0.7896776,0.001595357,0.1660171,0.00133476,0.002005123,0.0007244183,0.001615386,0.0005695212,0.03646089],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007113591,"threshold_uncertainty_score":0.02379739,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04133604880233874,"score_gpt":0.3286701684438024,"score_spread":0.2873341196414637,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}