{"id":"https://openalex.org/W7214748744","doi":"https://doi.org/10.48550/arxiv.2609.34057","title":"On the residual finiteness of the non-abelian tensor square $G \\otimes G$, the non-abelian exterior square $G \\wedge G$ and the weak commutativity construction $\\X(G)$","display_name":"On the residual finiteness of the non-abelian tensor square $G \\otimes G$, the non-abelian exterior square $G \\wedge G$ and the weak commutativity construction $\\X(G)$","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214748744","doi":"https://doi.org/10.48550/arxiv.2609.34057"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34057","pdf_url":"https://arxiv.org/pdf/2609.34057","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/2609.34057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153412586","display_name":"Ayrton Anjos Teixeira","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Teixeira, Ayrton Anjos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120546344","display_name":"Lucas Barroso Rocha","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rocha, Lucas Barroso","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000268378","display_name":"Dessislava H. Kochloukova","orcid":"https://orcid.org/0000-0001-5322-978X","observed_orcids":["https://orcid.org/0000-0001-5322-978X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kochloukova, Dessislava H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10849","display_name":"Finite Group Theory Research","score":0.8032000064849854,"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":0.8032000064849854,"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":0.15929999947547913,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.008999999612569809,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/residual-finiteness","display_name":"residual finiteness","score":0.8799999952316284},{"id":"https://openalex.org/keywords/profinite-completion","display_name":"profinite completion","score":0.925000011920929},{"id":"https://openalex.org/keywords/second-homology","display_name":"second homology","score":0.7720000147819519},{"id":"https://openalex.org/keywords/finitely-presented-groups","display_name":"finitely presented groups","score":0.8379999995231628},{"id":"https://openalex.org/keywords/metabelian-groups","display_name":"metabelian groups","score":0.9900000095367432}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8087000250816345},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7386000156402588},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6342999935150146},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.621399998664856},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5584999918937683},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5175999999046326},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C41678559","wikidata":"https://www.wikidata.org/wiki/Q7700713","display_name":"Tensor product of algebras","level":5,"score":0.27959999442100525},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","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":0.260699987411499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25459998846054077},{"id":"https://openalex.org/C101783463","wikidata":"https://www.wikidata.org/wiki/Q3406761","display_name":"Tensor product of modules","level":5,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34057","pdf_url":"https://arxiv.org/pdf/2609.34057","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.2609.34057","doi":"https://doi.org/10.48550/arxiv.2609.34057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34057","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:2609.34057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34057","pdf_url":"https://arxiv.org/pdf/2609.34057","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/W7214748744.pdf","grobid_xml":"https://content.openalex.org/works/W7214748744.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4287710382"],"related_works":["https://openalex.org/W7221042528","https://openalex.org/W2304579103","https://openalex.org/W7220437861","https://openalex.org/W2300226866","https://openalex.org/W2746589943","https://openalex.org/W2068959271","https://openalex.org/W2048448132","https://openalex.org/W2052326948","https://openalex.org/W4415950407","https://openalex.org/W1967516660"],"abstract_inverted_index":{"We":[0,46,98],"prove":[1,79],"that":[2,48,80],"if":[3,49,81],"$G$":[4,50,82],"is":[5,11,33,43,51,95],"a":[6,52,84,100],"residually":[7,44,75,96,111],"finite":[8],"group,":[9],"$\\widehat{G}$":[10],"its":[12],"profinite":[13],"completion":[14],"and":[15,66],"the":[16,27,36,59,67,90,103],"map":[17,29],"$H_2(G,":[18],"\\mathbb{Z})":[19],"$":[20,21],"\\to":[22,31],"H_2(\\widehat{G},":[23],"\\widehat{\\mathbb{Z}}),$":[24],"induced":[25],"by":[26],"canonical":[28],"$G":[30,40,63,71,106],"\\widehat{G}$,":[32],"injective,":[34],"then":[35,57,89],"non-abelian":[37,60,68],"exterior":[38],"square":[39,70,105],"\\wedge":[41,72],"G$":[42,65,73,108],"finite.":[45,76,97,112],"show":[47],"finitely":[53,85],"presented":[54,86],"centre-by-metabelian":[55],"group":[56,88],"$\u03bd(G)$,":[58],"tensor":[61,69],"product":[62],"\\otimes":[64],"are":[74],"Furthermore":[77],"we":[78],"be":[83,110],"metabelian":[87],"weak":[91],"commutative":[92],"construction":[93],"$\\X(G)$":[94],"discuss":[99],"criterion":[101],"for":[102],"$q$-exterior":[104],"\\wedge^q":[107],"to":[109]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
