{"id":"https://openalex.org/W7224474342","doi":"https://doi.org/10.5281/zenodo.23734919","title":"Order-universal free subgroups and bi-order extension","display_name":"Order-universal free subgroups and bi-order extension","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224474342","doi":"https://doi.org/10.5281/zenodo.23734919"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23734919","doi":"https://doi.org/10.5281/zenodo.23734919","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23734919","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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23734919","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007326745","display_name":"Martino Lupini","orcid":"https://orcid.org/0000-0003-1588-7057","observed_orcids":["https://orcid.org/0000-0003-1588-7057"]},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Lupini, Martino","raw_affiliation_strings":["University of Bologna"],"raw_orcid":"https://orcid.org/0000-0003-1588-7057","affiliations":[{"raw_affiliation_string":"University of Bologna","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007326745"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9911999702453613,"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":0.9911999702453613,"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":0.0012000000569969416,"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":0.0007999999797903001,"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/free-subgroups","display_name":"free subgroups","score":0.7979999780654907},{"id":"https://openalex.org/keywords/normal-subgroups","display_name":"normal subgroups","score":0.8220000267028809},{"id":"https://openalex.org/keywords/free-by-cyclic-groups","display_name":"free-by-cyclic groups","score":0.8159999847412109},{"id":"https://openalex.org/keywords/monodromy-groups","display_name":"monodromy groups","score":0.8299999833106995},{"id":"https://openalex.org/keywords/cyclic-covers","display_name":"cyclic coverings","score":0.7300000190734863},{"id":"https://openalex.org/keywords/undecidability","display_name":"undecidability","score":0.8539999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8585000038146973},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.7831000089645386},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7214000225067139},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4894999861717224},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.48730000853538513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44350001215934753},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.44110000133514404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43309998512268066},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4138999879360199},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.31450000405311584},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.31200000643730164},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C95627345","wikidata":"https://www.wikidata.org/wiki/Q1138961","display_name":"Quotient group","level":4,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.23734919","doi":"https://doi.org/10.5281/zenodo.23734919","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23734919","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.23734920","doi":"https://doi.org/10.5281/zenodo.23734920","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23734920","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.23804006","doi":"https://doi.org/10.5281/zenodo.23804006","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23804006","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":"doi:10.5281/zenodo.23734919","doi":"https://doi.org/10.5281/zenodo.23734919","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23734919","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320323553","display_name":"Universit\u00e0 di Bologna","ror":"https://ror.org/01111rn36"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4393177896","https://openalex.org/W7164834345","https://openalex.org/W7212351466","https://openalex.org/W4414749554","https://openalex.org/W7137500035","https://openalex.org/W3021806002","https://openalex.org/W2776371597","https://openalex.org/W4404261611","https://openalex.org/W4389131951","https://openalex.org/W2056770116"],"abstract_inverted_index":{"We":[0,54],"construct":[1],"fixed":[2,121,126],"free":[3,25,96,109,144],"subgroups":[4,16],"along":[5],"which":[6],"every":[7,19,58],"prescribed":[8],"bi-order":[9],"extends":[10],"to":[11,37,57,63,74,77],"the":[12,50,106,137,141],"ambient":[13],"group.":[14],"Such":[15],"exist":[17],"inside":[18],"nontrivial":[20],"normal":[21],"subgroup":[22],"of":[23,27,119,143],"a":[24,125],"group":[26],"rank":[28],"two.":[29],"A":[30],"finite-support":[31],"localization":[32],"theorem":[33],"transfers":[34],"this":[35],"property":[36],"other":[38],"bi-orderable":[39,59],"groups,":[40,122],"using":[41],"one":[42,130],"visible":[43],"element":[44],"and":[45,76,86,129],"an":[46,78],"invariant":[47],"order":[48],"on":[49],"actual":[51],"intermediate":[52],"quotient.":[53],"apply":[55],"it":[56],"rank-two":[60],"free-by-cyclic":[61],"group,":[62],"higher-rank":[64],"monodromies":[65],"with":[66],"positive":[67],"real":[68],"homology":[69],"spectrum":[70],"not":[71],"entirely":[72],"equal":[73],"one,":[75],"explicit":[79],"IA":[80],"mapping":[81],"torus.":[82],"The":[83,133],"last":[84],"example":[85],"all":[87],"its":[88],"height":[89],"cyclic":[90],"covers":[91],"admit":[92],"no":[93],"compatible":[94],"cyclic-cover":[95],"quotient":[97],"in":[98,117,146],"any":[99],"integral":[100],"character":[101],"direction,":[102],"but":[103],"still":[104],"have":[105],"required":[107],"universal":[108],"subgroups.":[110],"Consequently":[111],"total":[112],"Bi-order":[113],"Extension":[114],"is":[115],"undecidable":[116],"each":[118],"these":[120],"already":[123],"for":[124],"finite":[127,147],"background":[128],"varying":[131],"word.":[132],"argument":[134],"also":[135],"distinguishes":[136],"order-transfer":[138],"problem":[139],"from":[140],"existence":[142],"quotients":[145],"covers.":[148],"GitHub":[149],"repository":[150]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-30T00:00:00"}