{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001690264,0.0001066938,0.0004319512,0.00003387145,0.00007238003,0.00001526942,0.0002100325,0.00009669592,0.00003770455],"category_scores_gemma":[0.0006994316,0.00006739618,0.0005690408,0.00017185,0.0001805313,0.0001142608,0.00004318729,0.0002146341,5.558167e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004066169,"about_ca_system_score_gemma":0.00007869588,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004840284,"about_ca_topic_score_gemma":0.00000371391,"domain_scores_codex":[0.9984667,0.0001216875,0.000700127,0.00007872746,0.0004720445,0.0001607043],"domain_scores_gemma":[0.9967417,0.002206645,0.0005396368,0.0001830883,0.0002673165,0.00006164225],"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":[0.0002809404,0.001208295,0.0005025933,0.00386335,0.0003592547,0.00000168702,0.007885116,0.0000923212,0.06613207,0.9096583,0.007751765,0.002264329],"study_design_scores_gemma":[0.001157965,0.0001586804,0.001534643,0.0002240585,0.0001766096,0.00005814921,0.0003983665,0.002495046,0.009196126,0.9845068,0.00002574142,0.00006784281],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.720674,0.00006511407,0.2775607,0.001055457,0.00003377271,0.0003232144,0.00002476071,0.000005337165,0.0002576402],"genre_scores_gemma":[0.8921459,0.000008222478,0.1075211,0.00001729089,0.00007424061,0.000003148398,6.192756e-7,0.00001828638,0.0002111935],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1714719,"threshold_uncertainty_score":0.2748336,"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."}}