{"id":"https://openalex.org/W7223314647","doi":"https://doi.org/10.48550/arxiv.2610.31601","title":"Groups satisfying the minimal condition on centralizers are complete co-analytic","display_name":"Groups satisfying the minimal condition on centralizers are complete co-analytic","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223314647","doi":"https://doi.org/10.48550/arxiv.2610.31601"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.31601","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31601","pdf_url":"https://arxiv.org/pdf/2610.31601","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/2610.31601","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159323787","display_name":"Hakk\u0131 Ka\u011fan Yumak","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yumak, Hakk\u0131 Ka\u011fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159323787"],"corresponding_institution_ids":[],"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9868000149726868,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9868000149726868,"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/T10849","display_name":"Finite Group Theory Research","score":0.002300000051036477,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.002300000051036477,"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/countable-groups","display_name":"countable groups","score":0.8379999995231628},{"id":"https://openalex.org/keywords/polish-spaces","display_name":"Polish spaces","score":0.656000018119812},{"id":"https://openalex.org/keywords/descriptive-set-theory","display_name":"descriptive set theory","score":0.8579999804496765},{"id":"https://openalex.org/keywords/group-classification","display_name":"group classification","score":0.30799999833106995},{"id":"https://openalex.org/keywords/centralizers","display_name":"centralizers","score":0.5590000152587891}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7476999759674072},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6722000241279602},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3677000105381012},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3497999906539917},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2815000116825104},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.31601","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31601","pdf_url":"https://arxiv.org/pdf/2610.31601","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.2610.31601","doi":"https://doi.org/10.48550/arxiv.2610.31601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.31601","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.31601","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31601","pdf_url":"https://arxiv.org/pdf/2610.31601","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223314647.pdf","grobid_xml":"https://content.openalex.org/works/W7223314647.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1539382740","https://openalex.org/W1993488464","https://openalex.org/W2050007657","https://openalex.org/W2346276151","https://openalex.org/W2950833806","https://openalex.org/W2976535319","https://openalex.org/W4415187328"],"related_works":["https://openalex.org/W2766359216","https://openalex.org/W4323066427","https://openalex.org/W2093794979","https://openalex.org/W4404370656","https://openalex.org/W2250740871","https://openalex.org/W2061036962","https://openalex.org/W2318877537","https://openalex.org/W1986585006","https://openalex.org/W1977324525","https://openalex.org/W2327902475"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"prove":[4],"that":[5],"the":[6,11,22],"set":[7],"of":[8,21,25,32],"groups":[9],"satisfying":[10],"minimal":[12],"condition":[13],"on":[14],"centralizers":[15],"is":[16],"a":[17,30],"complete":[18],"co-analytic":[19],"subset":[20],"Polish":[23],"space":[24],"countable":[26],"groups.":[27],"This":[28],"answers":[29],"question":[31],"Wesolek":[33],"and":[34],"Williams.":[35]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}