{"id":"https://openalex.org/W2002546805","doi":"https://doi.org/10.1007/s00493-008-2262-8","title":"On the critical pair theory in abelian groups: Beyond Chowla\u2019s Theorem","display_name":"On the critical pair theory in abelian groups: Beyond Chowla\u2019s Theorem","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W2002546805","doi":"https://doi.org/10.1007/s00493-008-2262-8","mag":"2002546805"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-008-2262-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-008-2262-8","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0603478","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yahya O. Hamidoune","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yahya O. Hamidoune","raw_affiliation_strings":["E. Combinatoire et Optimisation, Universit\u00e9 Pierre et Marie Curie (Paris 6), 4, place Jussieu, 75252, Paris Cedex 05, France"],"affiliations":[{"raw_affiliation_string":"E. Combinatoire et Optimisation, Universit\u00e9 Pierre et Marie Curie (Paris 6), 4, place Jussieu, 75252, Paris Cedex 05, France","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Oriol Serra","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Oriol Serra","raw_affiliation_strings":["Dept. Matem\u00e0tica Aplicada 4, Universitat Polit\u00e8cnica de Catalunya, Jordi Girona, 1, E-08034, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. Matem\u00e0tica Aplicada 4, Universitat Polit\u00e8cnica de Catalunya, Jordi Girona, 1, E-08034, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":null,"display_name":"Gilles Z\u00e9mor","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Z\u00e9mor","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 Bordeaux 1, 351, cours de la Liberation, F-33405, Talence Cedex, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 Bordeaux 1, 351, cours de la Liberation, F-33405, Talence Cedex, France","institution_ids":["https://openalex.org/I4210166017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.527,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.62511374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":"4","first_page":"441","last_page":"467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.7458999752998352,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.7458999752998352,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.1809999942779541,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.013299999758601189,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/abelian-group","display_name":"Abelian group","score":0.8628000020980835},{"id":"https://openalex.org/keywords/elementary-abelian-group","display_name":"Elementary abelian group","score":0.515999972820282},{"id":"https://openalex.org/keywords/rank-of-an-abelian-group","display_name":"Rank of an abelian group","score":0.44670000672340393},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3506999909877777},{"id":"https://openalex.org/keywords/abelian-category","display_name":"Abelian category","score":0.3400999903678894},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.336899995803833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8989999890327454},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8628000020980835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5577999949455261},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.515999972820282},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.44670000672340393},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4302000105381012},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.335999995470047},{"id":"https://openalex.org/C188204562","wikidata":"https://www.wikidata.org/wiki/Q5275281","display_name":"Difference set","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.32409998774528503},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C163572010","wikidata":"https://www.wikidata.org/wiki/Q2912125","display_name":"G-module","level":4,"score":0.26840001344680786},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.26269999146461487}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00493-008-2262-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-008-2262-8","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0603478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0603478","pdf_url":"https://arxiv.org/pdf/math/0603478","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"},{"id":"pmh:oai:HAL:hal-00181453v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00181453","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorica, 2008, 28 (4), pp.441-467. ⟨10.1007/s00493-008-2262-8⟩","raw_type":"Journal articles"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/116949","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/116949","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/193275","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/193275","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0603478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0603478","pdf_url":"https://arxiv.org/pdf/math/0603478","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1994786975","https://openalex.org/W2005815733","https://openalex.org/W2010386855","https://openalex.org/W2034012450","https://openalex.org/W2045081006","https://openalex.org/W2050654150","https://openalex.org/W2051793589","https://openalex.org/W2065862555","https://openalex.org/W2067005190","https://openalex.org/W2068854759","https://openalex.org/W2069842544","https://openalex.org/W2086777570","https://openalex.org/W2086954015","https://openalex.org/W2092705071","https://openalex.org/W2131725427","https://openalex.org/W2157691323","https://openalex.org/W2479604145","https://openalex.org/W2912209775","https://openalex.org/W3009548514"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}