{"id":"https://openalex.org/W2081297737","doi":"https://doi.org/10.1090/s0025-5718-03-01612-0","title":"Orthomorphisms and the construction of projective planes","display_name":"Orthomorphisms and the construction of projective planes","publication_year":2003,"publication_date":"2003-07-31","ids":{"openalex":"https://openalex.org/W2081297737","doi":"https://doi.org/10.1090/s0025-5718-03-01612-0","mag":"2081297737"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-03-01612-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01612-0","pdf_url":"https://www.ams.org/mcom/2004-73-247/S0025-5718-03-01612-0/S0025-5718-03-01612-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2004-73-247/S0025-5718-03-01612-0/S0025-5718-03-01612-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031529103","display_name":"Felix Lazebnik","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Felix Lazebnik","raw_affiliation_strings":["Department of Mathematical Sciences, Ewing Building, University of Delaware, Newark, Delaware 19716"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Ewing Building, University of Delaware, Newark, Delaware 19716","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084708925","display_name":"Andrew Thomason","orcid":"https://orcid.org/0000-0002-1805-4221"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Thomason","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom","Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom","institution_ids":[]},{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1038,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.74146586,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"73","issue":"247","first_page":"1547","last_page":"1558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8278325796127319},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.7590461373329163},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6191994547843933},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6007859706878662},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5874934196472168},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.580744743347168},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4921988546848297},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.46928298473358154},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4673514664173126},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4661622643470764},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4617495834827423},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3894481062889099},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3390289545059204},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32792845368385315},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06286144256591797}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8278325796127319},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.7590461373329163},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6191994547843933},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6007859706878662},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5874934196472168},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.580744743347168},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4921988546848297},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.46928298473358154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4673514664173126},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4661622643470764},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4617495834827423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3894481062889099},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3390289545059204},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32792845368385315},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06286144256591797},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-03-01612-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01612-0","pdf_url":"https://www.ams.org/mcom/2004-73-247/S0025-5718-03-01612-0/S0025-5718-03-01612-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.407.7918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.407.7918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.udel.edu/~lazebnik/papers/thomlazB.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.7275","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.7275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2004-73-247/S0025-5718-03-01612-0/S0025-5718-03-01612-0.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-03-01612-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01612-0","pdf_url":"https://www.ams.org/mcom/2004-73-247/S0025-5718-03-01612-0/S0025-5718-03-01612-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5799999833106995}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320184","display_name":"London Mathematical Society","ror":"https://ror.org/01r1e1h27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2081297737.pdf","grobid_xml":"https://content.openalex.org/works/W2081297737.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1510730180","https://openalex.org/W1533880012","https://openalex.org/W1563907129","https://openalex.org/W1599335667","https://openalex.org/W1974903751","https://openalex.org/W2000233027","https://openalex.org/W2017689683","https://openalex.org/W2019022567","https://openalex.org/W2019885050","https://openalex.org/W2029316744","https://openalex.org/W2034869671","https://openalex.org/W2044472948","https://openalex.org/W2047680487","https://openalex.org/W2048958542","https://openalex.org/W2051396760","https://openalex.org/W2131628483","https://openalex.org/W2912810145","https://openalex.org/W2915069140","https://openalex.org/W3043060850","https://openalex.org/W4210390212","https://openalex.org/W4213144066","https://openalex.org/W4234795663","https://openalex.org/W4246611826","https://openalex.org/W4252352650","https://openalex.org/W4299667239"],"related_works":["https://openalex.org/W2114124567","https://openalex.org/W2998724919","https://openalex.org/W161787318","https://openalex.org/W1997883919","https://openalex.org/W1819644680","https://openalex.org/W3122644328","https://openalex.org/W2164080590","https://openalex.org/W1019837216","https://openalex.org/W1670912924","https://openalex.org/W2053779199"],"abstract_inverted_index":{"We":[0],"discuss":[1],"a":[2,19,55],"simple":[3],"computational":[4],"method":[5,86],"for":[6],"the":[7,27,39,47,51,60,85,90,97,102],"construction":[8,62],"of":[9,22,29,42,50,57,69,83,89,96,107],"finite":[10],"projective":[11],"planes.":[12,37],"The":[13,66],"planes":[14,41,68,75,79,93],"so":[15],"constructed":[16],"all":[17,64],"possess":[18],"special":[20],"group":[21,28,49,56],"automorphisms":[23],"which":[24],"we":[25],"call":[26],"translations,":[30,58],"but":[31],"they":[32],"are":[33],"not":[34],"always":[35],"translation":[36],"Of":[38],"four":[40,73,91],"order":[43,70],"9,":[44],"three":[45,88],"admit":[46],"additive":[48],"field":[52],"$GF(9)$":[53],"as":[54],"and":[59,76,94],"present":[61],"yields":[63],"three.":[65],"known":[67],"16":[71],"comprise":[72],"self-dual":[74,92],"eighteen":[77],"other":[78],"(nine":[80],"dual":[81,99],"pairs);":[82],"these,":[84],"gives":[87],"six":[95],"nine":[98],"pairs,":[100],"including":[101],"\u00e2\u0080\u009csporadic\u00e2\u0080\u009d":[103],"(not":[104],"translation)":[105],"plane":[106],"Mathon.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
