{"id":"https://openalex.org/W2112246751","doi":"https://doi.org/10.1142/s0218196715500228","title":"Fixed subgroups are compressed in surface groups","display_name":"Fixed subgroups are compressed in surface groups","publication_year":2015,"publication_date":"2015-06-04","ids":{"openalex":"https://openalex.org/W2112246751","doi":"https://doi.org/10.1142/s0218196715500228","mag":"2112246751"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715500228","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500228","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2117/77518","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100381850","display_name":"Qiang Zhang","orcid":"https://orcid.org/0000-0001-6332-5476"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiang Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108117742","display_name":"Enric Ventura","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Enric Ventura","raw_affiliation_strings":["Department of Applied Mathematics III, Universitat Polit\u00e8cnica de Catalunya, Manresa, Barcelona 08242, Catalonia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics III, Universitat Polit\u00e8cnica de Catalunya, Manresa, Barcelona 08242, Catalonia, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020141076","display_name":"Jianchun Wu","orcid":"https://orcid.org/0000-0001-9777-0041"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]},{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN","ES"],"is_corresponding":false,"raw_author_name":"Jianchun Wu","raw_affiliation_strings":["Department of Applied Mathematics III, Universitat Polit\u00e8cnica de Catalunya, Manresa, Barcelona 08242, Catalonia, Spain","Department of Mathematics, Soochow University, Suzhou 215006, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics III, Universitat Polit\u00e8cnica de Catalunya, Manresa, Barcelona 08242, Catalonia, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Department of Mathematics, Soochow University, Suzhou 215006, P. R. China","institution_ids":["https://openalex.org/I3923682"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100381850"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":1.058,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.75920929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"25","issue":"05","first_page":"865","last_page":"887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9939000010490417,"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/T11567","display_name":"semigroups and automata theory","score":0.9904000163078308,"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":0.9347729682922363},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.7491768598556519},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6629867553710938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5769689083099365},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5660405158996582},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5458508133888245},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.529984712600708},{"id":"https://openalex.org/keywords/maximal-subgroup","display_name":"Maximal subgroup","score":0.5042494535446167},{"id":"https://openalex.org/keywords/free-group","display_name":"Free group","score":0.43524035811424255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39551034569740295},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3925780951976776},{"id":"https://openalex.org/keywords/normal-subgroup","display_name":"Normal subgroup","score":0.18838739395141602},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17013901472091675},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.141386479139328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9347729682922363},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.7491768598556519},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6629867553710938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5769689083099365},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5660405158996582},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5458508133888245},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.529984712600708},{"id":"https://openalex.org/C76739243","wikidata":"https://www.wikidata.org/wiki/Q16908484","display_name":"Maximal subgroup","level":4,"score":0.5042494535446167},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.43524035811424255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39551034569740295},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3925780951976776},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.18838739395141602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17013901472091675},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.141386479139328},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196715500228","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500228","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"},{"id":"pmh:oai:recercat.cat:2072/300549","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/77518","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/77518","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/77518","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:recercat.cat:2072/300549","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/77518","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W576678118","https://openalex.org/W580052950","https://openalex.org/W770864251","https://openalex.org/W1516116134","https://openalex.org/W1552373856","https://openalex.org/W1964073377","https://openalex.org/W1974993663","https://openalex.org/W1975198066","https://openalex.org/W1986256453","https://openalex.org/W2002680896","https://openalex.org/W2002947378","https://openalex.org/W2034592120","https://openalex.org/W2049373129","https://openalex.org/W2061071363","https://openalex.org/W2061283920","https://openalex.org/W2094670490","https://openalex.org/W2169722656","https://openalex.org/W2327166707","https://openalex.org/W4231353887","https://openalex.org/W4240028494","https://openalex.org/W4292101339","https://openalex.org/W4312819332","https://openalex.org/W4312932108"],"related_works":["https://openalex.org/W3033412122","https://openalex.org/W4247247709","https://openalex.org/W2952950137","https://openalex.org/W2951646498","https://openalex.org/W2012948140","https://openalex.org/W4297914611","https://openalex.org/W4244786252","https://openalex.org/W2050743975","https://openalex.org/W1972047335","https://openalex.org/W2153463061"],"abstract_inverted_index":{"For":[0],"a":[1,61,91],"compact":[2],"surface":[3,74,87],"\u03a3":[4],"(orientable":[5],"or":[6,11],"not,":[7],"and":[8,72,86,89],"with":[9],"boundary":[10],"not),":[12],"we":[13,59],"show":[14],"that":[15,97],"the":[16,57,66],"fixed":[17],"subgroup,":[18],"Fix":[19,40,48,100],"\u212c,":[20],"of":[21,25,27,82,93],"any":[22,46],"family":[23],"\u212c":[24,49],"endomorphisms":[26],"\u03c0":[28,34,53],"1":[29,35,54],"(\u03a3)":[30],"is":[31],"compressed":[32],"in":[33],"(\u03a3),":[36],"i.e.":[37],"rk":[38,43,98,103],"(":[39,99],"\u212c)":[41],"\u2264":[42,50,52,102],"(H)":[44],"for":[45,70,73,105],"subgroup":[47],"H":[51],"(\u03a3).":[55],"On":[56],"way,":[58],"give":[60,90],"partial":[62],"positive":[63],"solution":[64],"to":[65],"inertia":[67],"conjecture,":[68],"both":[69],"free":[71,85],"groups.":[75],"We":[76],"also":[77],"investigate":[78],"direct":[79],"products,":[80],"G,":[81],"finitely":[83],"many":[84],"groups,":[88],"characterization":[92],"when":[94],"G":[95],"satisfies":[96],"\u03d5)":[101],"(G)":[104],"every":[106],"\u03d5":[107],"\u2208":[108],"Aut":[109],"(G).":[110]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
