{"id":"https://openalex.org/W3037137092","doi":"https://doi.org/10.1142/s0218196709005482","title":"BUCHSTEINER LOOPS","display_name":"BUCHSTEINER LOOPS","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W3037137092","doi":"https://doi.org/10.1142/s0218196709005482","mag":"3037137092"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005482","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005482","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026416089","display_name":"Piroska Cs\u00f6rg\u0151","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"PIROSKA CS\u00d6RG\u0150","raw_affiliation_strings":["Department of Mathematics, E\u00f6tv\u00f6s University, P\u00e1zm\u00e1ny P\u00e9ter S\u00e9t\u00f6ny 1/C, H-1117 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, E\u00f6tv\u00f6s University, P\u00e1zm\u00e1ny P\u00e9ter S\u00e9t\u00f6ny 1/C, H-1117 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045712903","display_name":"Ale\u0161 Dr\u00e1pal","orcid":"https://orcid.org/0000-0002-3879-7874"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"ALE\u0160 DR\u00c1PAL","raw_affiliation_strings":["Department of Mathematics, Charles University, Sokolovsk\u00e1 83, 186 75 Praha 8, Czech Rep"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Charles University, Sokolovsk\u00e1 83, 186 75 Praha 8, Czech Rep","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059332408","display_name":"Michael Kinyon","orcid":"https://orcid.org/0000-0002-5227-8632"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"MICHAEL K. KINYON","raw_affiliation_strings":["Department of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, Colorado 80208, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, Colorado 80208, U.S.A","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026416089"],"corresponding_institution_ids":["https://openalex.org/I106118109"],"apc_list":null,"apc_paid":null,"fwci":1.55,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83061129,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"08","first_page":"1049","last_page":"1088"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9934999942779541,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/mathematics","display_name":"Mathematics","score":0.9246644973754883},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.8088805675506592},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7082478404045105},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.7023046016693115},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.6044142246246338},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5345194935798645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4841242730617523},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.426333487033844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40517106652259827},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05179908871650696}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9246644973754883},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8088805675506592},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7082478404045105},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7023046016693115},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.6044142246246338},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5345194935798645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4841242730617523},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.426333487033844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40517106652259827},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05179908871650696},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005482","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005482","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1543045104","https://openalex.org/W1564749955","https://openalex.org/W1574042277","https://openalex.org/W1586207751","https://openalex.org/W1968055118","https://openalex.org/W1990465650","https://openalex.org/W2018508809","https://openalex.org/W2037111685","https://openalex.org/W2038134165","https://openalex.org/W2040493278","https://openalex.org/W2041332430","https://openalex.org/W2046932407","https://openalex.org/W2067513056","https://openalex.org/W2069642751","https://openalex.org/W2084256180","https://openalex.org/W2133516196","https://openalex.org/W2154245668","https://openalex.org/W2334904592","https://openalex.org/W2753518863","https://openalex.org/W4205421050","https://openalex.org/W4249735382"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W4297742300","https://openalex.org/W4295096867","https://openalex.org/W4291557013"],"abstract_inverted_index":{"Buchsteiner":[0,23],"loops":[1],"are":[2],"those":[3],"which":[4],"satisfy":[5],"the":[6,40],"identity":[7],"x":[8],"\\":[9],"(xy":[10],"\u00b7":[11,15],"z)":[12],"=":[13],"(y":[14],"zx)":[16],"/":[17],"x.":[18],"We":[19],"show":[20],"that":[21],"a":[22],"loop":[24],"modulo":[25],"its":[26],"nucleus":[27],"is":[28],"an":[29,37],"abelian":[30],"group":[31],"of":[32],"exponent":[33],"four,":[34],"and":[35],"construct":[36],"example":[38],"where":[39],"factor":[41],"achieves":[42],"this":[43],"exponent.":[44]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-07-02T00:00:00"}