{"id":"https://openalex.org/W2947291051","doi":"https://doi.org/10.1142/s021819672140004x","title":"Sums of element orders in groups of odd order","display_name":"Sums of element orders in groups of odd order","publication_year":2021,"publication_date":"2021-06-14","ids":{"openalex":"https://openalex.org/W2947291051","doi":"https://doi.org/10.1142/s021819672140004x","mag":"2947291051"},"language":"en","primary_location":{"id":"doi:10.1142/s021819672140004x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672140004x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.12291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011872468","display_name":"Marcel Herzog","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Marcel Herzog","raw_affiliation_strings":["School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel","School of Mathematical Sciences, Tel Aviv University Ramat Aviv, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University Ramat Aviv, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012456295","display_name":"Patrizia Longobardi","orcid":"https://orcid.org/0000-0002-7153-5243"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Patrizia Longobardi","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy","institution_ids":["https://openalex.org/I131729948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017436855","display_name":"Mercede Maj","orcid":"https://orcid.org/0000-0001-7010-5391"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Mercede Maj","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Salerno, via Giovanni Paolo II, 132, Fisciano (Salerno) 84084, Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011872468"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.6464,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54773414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"06","first_page":"1049","last_page":"1063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T11130","display_name":"Coding theory and cryptography","score":0.9896000027656555,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9810000061988831,"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/order","display_name":"Order (exchange)","score":0.8117368221282959},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7330267429351807},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6278990507125854},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6244406700134277},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.6045551300048828},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5740317106246948},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5498098731040955},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5374830961227417},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.46788448095321655},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40185973048210144},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06306669116020203}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.8117368221282959},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7330267429351807},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6278990507125854},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6244406700134277},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.6045551300048828},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5740317106246948},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5498098731040955},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5374830961227417},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.46788448095321655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40185973048210144},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06306669116020203},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s021819672140004x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672140004x","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"},{"id":"pmh:oai:arXiv.org:1905.12291","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.12291","pdf_url":"https://arxiv.org/pdf/1905.12291","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":"","raw_type":"text"},{"id":"mag:2947291051","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.12291","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1905.12291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.12291","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.12291","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.12291","pdf_url":"https://arxiv.org/pdf/1905.12291","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2573627744","display_name":null,"funder_award_id":"GNSAGA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320324133","display_name":"Universit\u00e0 degli Studi di Salerno","ror":"https://ror.org/0192m2k53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2947291051.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1980378955","https://openalex.org/W2012860839","https://openalex.org/W2031358693","https://openalex.org/W2032971395","https://openalex.org/W2068528259","https://openalex.org/W2093497308","https://openalex.org/W2140025044","https://openalex.org/W2158949661","https://openalex.org/W2166351687","https://openalex.org/W2329436721","https://openalex.org/W2345504666","https://openalex.org/W2734391510","https://openalex.org/W2810953164","https://openalex.org/W2912996409","https://openalex.org/W2916408298","https://openalex.org/W2962964556","https://openalex.org/W3073717275","https://openalex.org/W4205325251"],"related_works":["https://openalex.org/W2408464169","https://openalex.org/W1492157673","https://openalex.org/W1995573917","https://openalex.org/W1978180153","https://openalex.org/W2161636129","https://openalex.org/W2963397267","https://openalex.org/W2950918677","https://openalex.org/W1518932649","https://openalex.org/W2603377004","https://openalex.org/W2359264276","https://openalex.org/W1995658240","https://openalex.org/W2916408298","https://openalex.org/W2952876291","https://openalex.org/W2952740489","https://openalex.org/W1979006027","https://openalex.org/W2355768627","https://openalex.org/W2741249845","https://openalex.org/W2522671262","https://openalex.org/W2951547478","https://openalex.org/W2952870569"],"abstract_inverted_index":{"For":[0],"a":[1,26],"finite":[2],"group":[3,36],"[Formula:":[4,8,18,22,30,39,46,54,64,68,75,82,95,105,113,118,125,129],"see":[5,9,19,23,31,40,47,55,65,69,76,83,96,106,114,119,126,130],"text],":[6,66],"let":[7,29],"text]":[10,24,32,48,56,70,77,97,107,115,120,127,131],"denote":[11],"the":[12,34,50,58,90,99,109],"sum":[13],"of":[14,17,37,53,60,62,80,94,101,103,111,116,124],"element":[15],"orders":[16],"text].":[20,41,84],"If":[21],"is":[25,43,49,78,132],"positive":[27],"integer":[28],"be":[33],"cyclic":[35,79],"order":[38,63,81,104,117],"It":[42],"known":[44],"that":[45],"maximum":[51],"value":[52,93,123],"on":[57,98],"set":[59,100],"groups":[61,102,112],"and":[67,72,108],"if":[71,74],"only":[73],"In":[85],"this":[86,122],"paper,":[87],"we":[88],"investigate":[89],"second":[91],"largest":[92],"structure":[110],"with":[121],"when":[128],"odd.":[133]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}