{"id":"https://openalex.org/W7207836346","doi":"https://doi.org/10.48550/arxiv.2610.12087","title":"Group maps on initial intervals","display_name":"Group maps on initial intervals","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7207836346","doi":"https://doi.org/10.48550/arxiv.2610.12087"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.12087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12087","pdf_url":"https://arxiv.org/pdf/2610.12087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.12087","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101873523","display_name":"John M. Campbell","orcid":"https://orcid.org/0009-0003-8770-7788","observed_orcids":["https://orcid.org/0009-0003-8770-7788"]},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Campbell, John M.","raw_affiliation_strings":["Department of Mathematics and Statistics Dalhousie University Halifax , NS B3H 4R2 Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics Dalhousie University Halifax , NS B3H 4R2 Canada","institution_ids":["https://openalex.org/I129902397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101873523"],"corresponding_institution_ids":["https://openalex.org/I129902397"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.19619999825954437,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.19619999825954437,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10849","display_name":"Finite Group Theory Research","score":0.17810000479221344,"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":0.17000000178813934,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-functions","display_name":"multiplicative functions","score":0.6320000290870667},{"id":"https://openalex.org/keywords/abelian-groups","display_name":"abelian groups","score":0.8220000267028809},{"id":"https://openalex.org/keywords/injective-functions","display_name":"injective functions","score":0.5559999942779541}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8190000057220459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7943999767303467},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7386000156402588},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5964999794960022},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5375999808311462},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35920000076293945},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2329999953508377}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.12087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12087","pdf_url":"https://arxiv.org/pdf/2610.12087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.12087","doi":"https://doi.org/10.48550/arxiv.2610.12087","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.12087","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22269671","doi":"https://doi.org/10.5281/zenodo.22269671","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22269671","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22269672","doi":"https://doi.org/10.5281/zenodo.22269672","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22269672","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.12087","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12087","pdf_url":"https://arxiv.org/pdf/2610.12087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207836346.pdf","grobid_xml":"https://content.openalex.org/works/W7207836346.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4210570486","https://openalex.org/W2073829469","https://openalex.org/W2033558312","https://openalex.org/W2006965986","https://openalex.org/W137443868","https://openalex.org/W2792152669","https://openalex.org/W2070302103","https://openalex.org/W3143651652","https://openalex.org/W1698471743","https://openalex.org/W7097737659"],"abstract_inverted_index":{"Let":[0,7],"$S$":[1],"denote":[2],"a":[3,10,20,72],"$k$-subset":[4],"of":[5,13],"$\\mathbb{Z}$.":[6],"$G$":[8,66],"be":[9],"(multiplicative)":[11],"group":[12],"size":[14],"$k$.":[15],"Assume":[16],"that":[17,26,30,55],"there":[18],"exists":[19],"function":[21],"$\\varphi\\colon":[22],"S":[23],"\\to":[24],"G$":[25],"is":[27,67],"injective":[28],"and":[29,40,52,84,118],"satisfies":[31],"the":[32,112,116],"following:":[33],"If":[34],"$x,":[35],"y,":[36],"z":[37],"\\in":[38],"S$":[39],"$z":[41],"=":[42,46,58],"xy$,":[43],"then":[44,65],"$\\varphi(z)":[45],"\\varphi(x)":[47],"\\varphi(y)$.":[48],"In":[49],"1990,":[50],"Forcade":[51],"Pollington":[53],"conjectured":[54],"if":[56],"$S":[57],"\\{":[59],"1,":[60],"2,":[61],"\\ldots,":[62],"k":[63],"\\}$,":[64],"abelian.":[68],"This":[69],"has":[70],"been":[71,97],"long-standing":[73],"conjecture":[74,114],"highlighted":[75],"by":[76,99],"Richard":[77],"K.\\":[78],"Guy":[79],"as":[80],"an":[81],"unsolved":[82],"problem,":[83],"this":[85],"problem":[86],"appears":[87],"to":[88],"have":[89],"remained":[90],"open,":[91],"with":[92],"its":[93],"open":[94],"status":[95],"having":[96],"noted":[98],"Caicedo":[100],"et":[101],"al.\\":[102],"in":[103,110,115,119],"2021":[104],"[Electron.":[105],"J.":[106],"Combin.].":[107],"We":[108],"succeed":[109],"proving":[111],"Forcade--Pollington":[113],"affirmative":[117],"full":[120],"generality.":[121]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-04T00:00:00"}
