{"id":"https://openalex.org/W2193887203","doi":"https://doi.org/10.1142/s021819671550023x","title":"On Moufang loops that are abelian groups over the nucleus","display_name":"On Moufang loops that are abelian groups over the nucleus","publication_year":2015,"publication_date":"2015-06-24","ids":{"openalex":"https://openalex.org/W2193887203","doi":"https://doi.org/10.1142/s021819671550023x","mag":"2193887203"},"language":"en","primary_location":{"id":"doi:10.1142/s021819671550023x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671550023x","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/I120832542","display_name":"Eszterhazy Karoly Catholic University","ror":"https://ror.org/004gfgx38","country_code":"HU","type":"education","lineage":["https://openalex.org/I120832542"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Piroska Cs\u00f6rg\u0151","raw_affiliation_strings":["Institute of Mathematics, Eszterh\u00e1zy K\u00e1roly College, Eger, Le\u00e1nyka u. 4, H-3300, Hungary"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Eszterh\u00e1zy K\u00e1roly College, Eger, Le\u00e1nyka u. 4, H-3300, Hungary","institution_ids":["https://openalex.org/I120832542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071962445","display_name":"M. L. Merlini Giuliani","orcid":null},"institutions":[{"id":"https://openalex.org/I71715416","display_name":"Universidade Federal do ABC","ror":"https://ror.org/028kg9j04","country_code":"BR","type":"education","lineage":["https://openalex.org/I71715416"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Maria L. Merlini Giuliani","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal do ABC, Rua Santa Ad\u00e9lia 166 Santo Andr\u00e9, SP, 09210-170, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal do ABC, Rua Santa Ad\u00e9lia 166 Santo Andr\u00e9, SP, 09210-170, Brazil","institution_ids":["https://openalex.org/I71715416"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026416089"],"corresponding_institution_ids":["https://openalex.org/I120832542"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12115655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"05","first_page":"889","last_page":"897"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9904000163078308,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8599560856819153},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.8187195062637329},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.6064968109130859},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.5773231387138367},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5234313011169434},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4808517098426819},{"id":"https://openalex.org/keywords/nucleus","display_name":"Nucleus","score":0.465831458568573},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34841668605804443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06385841965675354},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.034905076026916504},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.030540525913238525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8599560856819153},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8187195062637329},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.6064968109130859},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5773231387138367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5234313011169434},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4808517098426819},{"id":"https://openalex.org/C2780723820","wikidata":"https://www.wikidata.org/wiki/Q1934178","display_name":"Nucleus","level":2,"score":0.465831458568573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34841668605804443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06385841965675354},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.034905076026916504},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.030540525913238525},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819671550023x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671550023x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2022749384","https://openalex.org/W2026279114","https://openalex.org/W2039190603","https://openalex.org/W2040493278","https://openalex.org/W2156431026","https://openalex.org/W2159047508","https://openalex.org/W3037137092","https://openalex.org/W4237207618","https://openalex.org/W4249735382"],"related_works":["https://openalex.org/W2114124567","https://openalex.org/W2998724919","https://openalex.org/W161787318","https://openalex.org/W1997883919","https://openalex.org/W1968682565","https://openalex.org/W2963982375","https://openalex.org/W2042372008","https://openalex.org/W2376326551","https://openalex.org/W3122198505","https://openalex.org/W4221160447"],"abstract_inverted_index":{"We":[0,37],"give":[1],"some":[2],"necessary":[3],"and":[4,29],"sufficient":[5],"conditions":[6],"for":[7,15],"the":[8,11,22,32,51,55],"equivalency":[9],"of":[10,41,54],"following":[12],"two":[13],"properties":[14,40],"a":[16,35],"Moufang":[17,42],"loop":[18],"Q:":[19],"Q":[20,30],"over":[21,31],"nucleus":[23],"Q/N":[24],"is":[25,34,49],"an":[26],"abelian":[27],"group":[28,53],"center":[33],"group.":[36],"study":[38],"those":[39],"loops":[43],"which":[44],"guarantee":[45],"that":[46],"L(y,":[47],"x)":[48],"in":[50],"automorphism":[52],"loop.":[56],"These":[57],"imply":[58],"numerous":[59],"statements,":[60],"among":[61],"them":[62],"there":[63],"are":[64],"well-known":[65],"old":[66],"results.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
