{"id":"https://openalex.org/W7125943318","doi":"https://doi.org/10.1016/j.apal.2026.103727","title":"Scott complexity of reduced Abelian p-groups","display_name":"Scott complexity of reduced Abelian p-groups","publication_year":2026,"publication_date":"2026-01-28","ids":{"openalex":"https://openalex.org/W7125943318","doi":"https://doi.org/10.1016/j.apal.2026.103727"},"language":"en","primary_location":{"id":"doi:10.1016/j.apal.2026.103727","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103727","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.apal.2026.103727","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068606143","display_name":"Rachael Alvir","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Rachael Alvir","raw_affiliation_strings":["University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada"],"raw_orcid":"https://orcid.org/0009-0008-8065-2143","affiliations":[{"raw_affiliation_string":"University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061005365","display_name":"Barbara F. Csima","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Barbara F. Csima","raw_affiliation_strings":["University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024319395","display_name":"Luke MacLean","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Luke MacLean","raw_affiliation_strings":["University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Mathematics Department, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068606143"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":{"value":3390,"currency":"USD","value_usd":3390},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24704724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"177","issue":"7","first_page":"103727","last_page":"103727"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.5828999876976013,"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":0.5828999876976013,"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":0.10580000281333923,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.07490000128746033,"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/abelian-group","display_name":"Abelian group","score":0.8838000297546387},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6974999904632568},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5626000165939331},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5376999974250793},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5109999775886536},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5047000050544739},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3452000021934509},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.34220001101493835}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8838000297546387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8166000247001648},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6974999904632568},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5626000165939331},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5109999775886536},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49959999322891235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4584999978542328},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.3310000002384186},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32850000262260437},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.32589998841285706},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.2964000105857849},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.2554999887943268},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.apal.2026.103727","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103727","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.apal.2026.103727","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.apal.2026.103727","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7559644256","display_name":null,"funder_award_id":"RGPIN-2024-04021","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1972311151","https://openalex.org/W2016314496","https://openalex.org/W2059318640","https://openalex.org/W2073805904","https://openalex.org/W2590309738","https://openalex.org/W2898117887","https://openalex.org/W2962709929","https://openalex.org/W3128766521","https://openalex.org/W4239460493"],"related_works":[],"abstract_inverted_index":{"Given":[0],"a":[1,57],"reduced":[2,66],"Abelian":[3,67],"p":[4,68],"-group,":[5],"we":[6,27,55],"give":[7,56],"an":[8,37,73],"upper":[9,31],"bound":[10,32],"on":[11,65,72],"the":[12,16,53,62],"Scott":[13,46],"complexity":[14,47],"of":[15,20,40,61,76],"group":[17],"in":[18],"terms":[19],"its":[21],"Ulm":[22],"invariants.":[23],"For":[24],"limit":[25],"ordinals,":[26],"show":[28],"that":[29],"this":[30],"is":[33],"tight.":[34],"This":[35],"gives":[36],"explicit":[38],"sequence":[39],"such":[41],"groups":[42],"with":[43],"arbitrarily":[44],"high":[45],"below":[48],"\u03c9":[49],"1":[50],".":[51,82],"Along":[52],"way,":[54],"largely":[58],"algebraic":[59],"characterization":[60],"back-and-forth":[63],"relations":[64],"-groups,":[69],"making":[70],"progress":[71],"open":[74],"problem":[75],"Ash":[77],"and":[78],"Knight's":[79],"from":[80],"[4]":[81]},"counts_by_year":[],"updated_date":"2026-02-13T13:36:01.753593","created_date":"2026-01-29T00:00:00"}