{"id":"https://openalex.org/W4210724715","doi":"https://doi.org/10.1142/s021819672250014x","title":"Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval","display_name":"Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval","publication_year":2022,"publication_date":"2022-01-31","ids":{"openalex":"https://openalex.org/W4210724715","doi":"https://doi.org/10.1142/s021819672250014x"},"language":"en","primary_location":{"id":"doi:10.1142/s021819672250014x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672250014x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057324575","display_name":"Takamichi Sato","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takamichi Sato","raw_affiliation_strings":["Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan","institution_ids":["https://openalex.org/I150744194"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057324575"],"corresponding_institution_ids":["https://openalex.org/I150744194"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10253772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"32","issue":"02","first_page":"289","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.996999979019165,"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":0.996999979019165,"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":0.978600025177002,"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/T11567","display_name":"semigroups and automata theory","score":0.9768999814987183,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9274564981460571},{"id":"https://openalex.org/keywords/unit-interval","display_name":"Unit interval","score":0.8270049095153809},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6370043158531189},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.582022488117218},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5672540664672852},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.5650540590286255},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5466036796569824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4642214775085449},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.46376869082450867},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.46098148822784424},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.4405447244644165},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4325670599937439},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38947558403015137},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36031603813171387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09893208742141724}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9274564981460571},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.8270049095153809},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6370043158531189},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.582022488117218},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5672540664672852},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.5650540590286255},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5466036796569824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4642214775085449},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.46376869082450867},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.46098148822784424},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.4405447244644165},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4325670599937439},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38947558403015137},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36031603813171387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09893208742141724},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819672250014x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672250014x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1908418828","https://openalex.org/W1984884268","https://openalex.org/W2033511865","https://openalex.org/W2063967677","https://openalex.org/W2079420233","https://openalex.org/W2962682637","https://openalex.org/W2963424842","https://openalex.org/W2963695734","https://openalex.org/W2963882960","https://openalex.org/W4205325251"],"related_works":["https://openalex.org/W2464700030","https://openalex.org/W1560475590","https://openalex.org/W4298192435","https://openalex.org/W4256002322","https://openalex.org/W1979611069","https://openalex.org/W2962708990","https://openalex.org/W2090054817","https://openalex.org/W2342553057","https://openalex.org/W2012455905","https://openalex.org/W1599639459"],"abstract_inverted_index":{"We":[0,36,110],"study":[1],"subgroups":[2,43,74],"of":[3,9,14,34,44,52,75,86,89],"the":[4,15,32,76,92],"group":[5,79,126],"[Formula:":[6,18,45,80,94,127],"see":[7,19,46,81,95,128],"text]":[8,20,47,82,96],"piecewise":[10],"linear":[11],"orientation-preserving":[12],"homeomorphisms":[13],"unit":[16],"interval":[17,93],"that":[21,83,113],"are":[22,49,84,117,121],"differentiable":[23],"everywhere":[24],"except":[25],"at":[26],"finitely":[27,53],"many":[28,54],"real":[29],"numbers,":[30],"under":[31],"operation":[33],"composition.":[35],"provide":[37],"a":[38,66,102,124],"criterion":[39],"for":[40,71],"any":[41,72],"two":[42,73,115],"which":[48],"direct":[50],"products":[51],"indecomposable":[55],"non-commutative":[56],"groups":[57],"to":[58,97],"be":[59,98],"non-isomorphic.":[60],"As":[61],"its":[62],"application,":[63],"we":[64],"give":[65],"necessary":[67],"and":[68,107],"sufficient":[69],"condition":[70],"R.":[77],"Thompson":[78],"stabilizers":[85,116],"finite":[87],"sets":[88],"numbers":[90],"in":[91],"isomorphic,":[99,118],"thus":[100],"solving":[101],"problem":[103],"by":[104],"G.":[105],"Golan":[106],"M.":[108],"Sapir.":[109],"also":[111],"show":[112],"if":[114],"then":[119],"they":[120],"conjugate":[122],"inside":[123],"certain":[125],"text].":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
