{"id":"https://openalex.org/W2055029817","doi":"https://doi.org/10.1112/s1461157010000173","title":"Searching for small simple automorphic loops","display_name":"Searching for small simple automorphic loops","publication_year":2011,"publication_date":"2011-08-01","ids":{"openalex":"https://openalex.org/W2055029817","doi":"https://doi.org/10.1112/s1461157010000173","mag":"2055029817"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157010000173","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157010000173","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9F17F36DC2496D812860E9E20EB9973F/S1461157010000173a.pdf/div-class-title-searching-for-small-simple-automorphic-loops-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9F17F36DC2496D812860E9E20EB9973F/S1461157010000173a.pdf/div-class-title-searching-for-small-simple-automorphic-loops-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kenneth W. Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I2803030221","display_name":"Abington Memorial Hospital","ror":"https://ror.org/03jgh1p68","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2803030221"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth W. Johnson","raw_affiliation_strings":["Penn State Abington, 1600 Woodland Rd, Abington PA 19001, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Penn State Abington, 1600 Woodland Rd, Abington PA 19001, USA","institution_ids":["https://openalex.org/I2803030221"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Michael K. Kinyon","orcid":null},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael K. Kinyon","raw_affiliation_strings":["Department of Mathematics, University of Denver, 2360 S Gaylord St, Denver Colorado 80112, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Denver, 2360 S Gaylord St, Denver Colorado 80112, USA","institution_ids":["https://openalex.org/I131651094"]}]},{"author_position":"middle","author":{"id":null,"display_name":"G\u00e1bor P. Nagy","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"G\u00e1bor P. Nagy","raw_affiliation_strings":["Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1 H-6720 Szeged, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1 H-6720 Szeged, Hungary","institution_ids":["https://openalex.org/I227486990"]}]},{"author_position":"last","author":{"id":null,"display_name":"Petr Vojt\u011bchovsk\u00fd","orcid":null},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Petr Vojt\u011bchovsk\u00fd","raw_affiliation_strings":["Department of Mathematics, University of Denver, 2360 S Gaylord St, Denver Colorado 80112, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Denver, 2360 S Gaylord St, Denver Colorado 80112, USA","institution_ids":["https://openalex.org/I131651094"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7347,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.69052909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":null,"first_page":"200","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.018799999728798866,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/automorphic-form","display_name":"Automorphic form","score":0.8924999833106995},{"id":"https://openalex.org/keywords/automorphic-l-function","display_name":"Automorphic L-function","score":0.8356000185012817},{"id":"https://openalex.org/keywords/langlands\u2013shahidi-method","display_name":"Langlands\u2013Shahidi method","score":0.6888999938964844},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.67330002784729},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.6381999850273132},{"id":"https://openalex.org/keywords/converse-theorem","display_name":"Converse theorem","score":0.6341000199317932}],"concepts":[{"id":"https://openalex.org/C132817261","wikidata":"https://www.wikidata.org/wiki/Q1134435","display_name":"Automorphic form","level":2,"score":0.8924999833106995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8755999803543091},{"id":"https://openalex.org/C202434901","wikidata":"https://www.wikidata.org/wiki/Q4826697","display_name":"Automorphic L-function","level":3,"score":0.8356000185012817},{"id":"https://openalex.org/C104559423","wikidata":"https://www.wikidata.org/wiki/Q6486192","display_name":"Langlands\u2013Shahidi method","level":3,"score":0.6888999938964844},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.67330002784729},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.6381999850273132},{"id":"https://openalex.org/C204591131","wikidata":"https://www.wikidata.org/wiki/Q5166461","display_name":"Converse theorem","level":3,"score":0.6341000199317932},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47279998660087585},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C176637632","wikidata":"https://www.wikidata.org/wiki/Q2993300","display_name":"Artin L-function","level":3,"score":0.3264000117778778},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/s1461157010000173","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157010000173","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9F17F36DC2496D812860E9E20EB9973F/S1461157010000173a.pdf/div-class-title-searching-for-small-simple-automorphic-loops-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1006.3886","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1006.3886","pdf_url":"https://arxiv.org/pdf/1006.3886","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1112/s1461157010000173","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157010000173","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9F17F36DC2496D812860E9E20EB9973F/S1461157010000173a.pdf/div-class-title-searching-for-small-simple-automorphic-loops-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2055029817.pdf","grobid_xml":"https://content.openalex.org/works/W2055029817.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W593714432","https://openalex.org/W1764899937","https://openalex.org/W1971775655","https://openalex.org/W1972206626","https://openalex.org/W1992521524","https://openalex.org/W2007274893","https://openalex.org/W2017284704","https://openalex.org/W2021375748","https://openalex.org/W2023310495","https://openalex.org/W2026279114","https://openalex.org/W2031686606","https://openalex.org/W2045878517","https://openalex.org/W2057091051","https://openalex.org/W2075240364","https://openalex.org/W2090821508","https://openalex.org/W2091665145","https://openalex.org/W2109179221","https://openalex.org/W2136915037","https://openalex.org/W2142124365","https://openalex.org/W2168805792","https://openalex.org/W2319934518","https://openalex.org/W2334904592","https://openalex.org/W2917362937","https://openalex.org/W4237207618","https://openalex.org/W4249735382","https://openalex.org/W4293259454","https://openalex.org/W6603897259","https://openalex.org/W6666986166"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"A":[1],"loop":[2,33,46,68,79],"is":[3,27,80],"(right)":[4,9],"automorphic":[5,32,45,60,67,78,81],"if":[6,82,85],"all":[7],"its":[8,86],"inner":[10],"mappings":[11],"are":[12,88],"automorphisms.":[13,89],"Using":[14],"the":[15,70],"classification":[16],"of":[17,20,34,47,56],"primitive":[18],"groups":[19],"small":[21],"degrees,":[22],"we":[23],"show":[24],"that":[25,65,75],"there":[26],"no":[28,42],"non-associative":[29,43,57],"simple":[30,44,58],"commutative":[31],"order":[35,48],"less":[36,49],"than":[37,50],"2":[38],"12":[39],",":[40],"and":[41,74,83],"2500.":[51],"We":[52,62],"obtain":[53],"numerous":[54],"examples":[55],"right":[59,77],"loops.":[61],"also":[63],"prove":[64],"every":[66],"has":[69],"antiautomorphic":[71],"inverse":[72],"property,":[73],"a":[76],"only":[84],"conjugations":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2016-06-24T00:00:00"}