{"id":"https://openalex.org/W7204111129","doi":"https://doi.org/10.48550/arxiv.2608.20472","title":"Free Burnside groups of large odd exponent have cost 1","display_name":"Free Burnside groups of large odd exponent have cost 1","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7204111129","doi":"https://doi.org/10.48550/arxiv.2608.20472"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20472","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20472","pdf_url":"https://arxiv.org/pdf/2608.20472","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/2608.20472","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115860759","display_name":"Miguel Donoso-Echenique","orcid":"https://orcid.org/0009-0007-1511-8107","observed_orcids":["https://orcid.org/0009-0007-1511-8107"]},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Donoso-Echenique, Miguel","raw_affiliation_strings":["University of M\u00fcnster , Einsteinstrasse 62 , M\u00fcnster 48149 , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of M\u00fcnster , Einsteinstrasse 62 , M\u00fcnster 48149 , Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147987659","display_name":"Eduardo Silva","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Silva, Eduardo","raw_affiliation_strings":["University of M\u00fcnster , Einsteinstrasse 62 , M\u00fcnster 48149 , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of M\u00fcnster , Einsteinstrasse 62 , M\u00fcnster 48149 , Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I22465464"],"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9229000210762024,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9229000210762024,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.02969999983906746,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.010999999940395355,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/free-burnside-groups","display_name":"free Burnside groups","score":0.9200000166893005},{"id":"https://openalex.org/keywords/hyperbolic-groups","display_name":"hyperbolic groups","score":0.7329999804496765},{"id":"https://openalex.org/keywords/torsion-free-groups","display_name":"torsion-free groups","score":0.8190000057220459},{"id":"https://openalex.org/keywords/l2-betti-numbers","display_name":"L2-Betti numbers","score":0.8769999742507935},{"id":"https://openalex.org/keywords/free-groups","display_name":"free groups","score":0.6420000195503235},{"id":"https://openalex.org/keywords/odd-exponents","display_name":"odd exponents","score":0.6669999957084656},{"id":"https://openalex.org/keywords/group-actions-on-trees","display_name":"group actions on trees","score":0.47099998593330383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7926999926567078},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7358999848365784},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.46560001373291016},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37139999866485596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3082999885082245},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.24269999563694}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20472","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20472","pdf_url":"https://arxiv.org/pdf/2608.20472","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.2608.20472","doi":"https://doi.org/10.48550/arxiv.2608.20472","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20472","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:2608.20472","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20472","pdf_url":"https://arxiv.org/pdf/2608.20472","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/W7204111129.pdf","grobid_xml":"https://content.openalex.org/works/W7204111129.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2070598006","https://openalex.org/W2896014663","https://openalex.org/W2961605278","https://openalex.org/W2786870243","https://openalex.org/W2030128136","https://openalex.org/W4412592273","https://openalex.org/W2949538838","https://openalex.org/W2128616758","https://openalex.org/W4361229215","https://openalex.org/W2770189262"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,35,52,57,82],"for":[3,44,84],"every":[4,45],"non-elementary":[5],"torsion-free":[6],"hyperbolic":[7],"group":[8,28,39],"$H$":[9,24],"and":[10,56,67,73],"sufficiently":[11,86],"large":[12,87],"odd":[13,46],"$n>1$,":[14],"the":[15,26,36],"quotient":[16],"$H/H^n$":[17],"has":[18,41],"cost":[19,42],"$1$.":[20],"In":[21],"particular,":[22],"when":[23],"is":[25,54],"free":[27,37],"of":[29,71],"rank":[30],"$m\\ge":[31],"2$,":[32],"we":[33],"obtain":[34],"Burnside":[38],"$B(m,n)$":[40,53],"$1$":[43],"exponent":[47],"$n\\geq":[48],"665$.":[49],"It":[50],"follows":[51],"anti-treeable,":[55],"its":[58],"first":[59],"$\\ell^2$-Betti":[60],"number":[61],"$\u03b2_1^{(2)}(B(m,n))$":[62],"vanishes.":[63],"The":[64],"latter":[65],"recovers":[66],"extends":[68],"a":[69],"result":[70],"Feldkamp":[72],"Kionke":[74],"[Proc.":[75],"Amer.":[76],"Math.":[77],"Soc.,":[78],"2023],":[79],"who":[80],"proved":[81],"$\u03b2_1^{(2)}(B(m,p))=0$":[83],"all":[85],"prime":[88],"exponents":[89],"$p$.":[90]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-25T00:00:00"}