{"id":"https://openalex.org/W2015107886","doi":"https://doi.org/10.1142/s0218196712500749","title":"AUTOMORPHISMS OF PARTIALLY COMMUTATIVE GROUPS II: COMBINATORIAL SUBGROUPS","display_name":"AUTOMORPHISMS OF PARTIALLY COMMUTATIVE GROUPS II: COMBINATORIAL SUBGROUPS","publication_year":2012,"publication_date":"2012-09-24","ids":{"openalex":"https://openalex.org/W2015107886","doi":"https://doi.org/10.1142/s0218196712500749","mag":"2015107886"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500749","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500749","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1106.2331","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"ANDREW J. DUNCAN","orcid":null},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"ANDREW J. DUNCAN","raw_affiliation_strings":["School of Mathematics &amp; Statistics, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics &amp; Statistics, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":null,"display_name":"VLADIMIR N. REMESLENNIKOV","orcid":null},"institutions":[{"id":"https://openalex.org/I269199756","display_name":"Omsk State University","ror":"https://ror.org/01k6vxj52","country_code":"RU","type":"education","lineage":["https://openalex.org/I269199756"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"VLADIMIR N. REMESLENNIKOV","raw_affiliation_strings":["Department of Mathematics, Omsk State University, 55-A Prospect Mira, Omsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Omsk State University, 55-A Prospect Mira, Omsk, Russia","institution_ids":["https://openalex.org/I269199756"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84884186"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.10053809,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"07","first_page":"1250074","last_page":"1250074"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.8550999760627747,"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":0.8550999760627747,"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":0.09070000052452087,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.01860000006854534,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/automorphism","display_name":"Automorphism","score":0.8087999820709229},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6468999981880188},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.45719999074935913},{"id":"https://openalex.org/keywords/direct-product","display_name":"Direct product","score":0.4194999933242798},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41519999504089355},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.39079999923706055},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.3905999958515167},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.3765999972820282},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.3707999885082245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9301999807357788},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8087999820709229},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6438000202178955},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.45719999074935913},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36070001125335693},{"id":"https://openalex.org/C50598534","wikidata":"https://www.wikidata.org/wiki/Q747027","display_name":"Characteristic subgroup","level":4,"score":0.3582000136375427},{"id":"https://openalex.org/C162619202","wikidata":"https://www.wikidata.org/wiki/Q4826703","display_name":"Automorphisms of the symmetric and alternating groups","level":3,"score":0.3248000144958496},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C134064494","wikidata":"https://www.wikidata.org/wiki/Q6664682","display_name":"Locally finite group","level":3,"score":0.31630000472068787},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C160826032","wikidata":"https://www.wikidata.org/wiki/Q286972","display_name":"p-group","level":3,"score":0.2962000072002411},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C143132287","wikidata":"https://www.wikidata.org/wiki/Q3492011","display_name":"Fitting subgroup","level":4,"score":0.25999999046325684},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.2581999897956848},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.2526000142097473},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196712500749","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500749","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:arXiv.org:1106.2331","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.2331","pdf_url":"https://arxiv.org/pdf/1106.2331","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1106.2331","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.2331","pdf_url":"https://arxiv.org/pdf/1106.2331","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G4212162790","display_name":null,"funder_award_id":"EP/F014945/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W11363830","https://openalex.org/W1503316946","https://openalex.org/W1556583142","https://openalex.org/W1753548755","https://openalex.org/W1979142405","https://openalex.org/W1987313842","https://openalex.org/W2017555772","https://openalex.org/W2025603014","https://openalex.org/W2026825318","https://openalex.org/W2038964297","https://openalex.org/W2047799821","https://openalex.org/W2050007657","https://openalex.org/W2057293780","https://openalex.org/W2057620257","https://openalex.org/W2074885793","https://openalex.org/W2089406551","https://openalex.org/W2090940258","https://openalex.org/W2104480106","https://openalex.org/W2120276971","https://openalex.org/W2121978727","https://openalex.org/W2148466810","https://openalex.org/W2148663533","https://openalex.org/W2168086402","https://openalex.org/W2323845175","https://openalex.org/W2333395501","https://openalex.org/W2962857491","https://openalex.org/W2963247182","https://openalex.org/W2963361157"],"related_works":[],"abstract_inverted_index":{"We":[0,109],"define":[1],"several":[2],"\"standard\"":[3],"subgroups":[4,22],"of":[5,11,26,35,45,49,72,84,90,101,104,107,124],"the":[6,32,46,58,95,105],"automorphism":[7],"group":[8,17],"Aut":[9,27,40,85,116],"(G)":[10,41,86,117],"a":[12,52,73,81,88,98,119],"partially":[13],"commutative":[14],"(right-angled":[15],"Artin)":[16],"and":[18],"use":[19],"these":[20],"standard":[21],"to":[23],"describe":[24],"decompositions":[25],"(G).":[28],"If":[29,67],"C":[30,62,68],"is":[31,118],"commutation":[33],"graph":[34],"G,":[36],"we":[37,75,79],"show":[38],"how":[39],"decomposes":[42],"in":[43,57],"terms":[44],"connected":[47],"components":[48],"C:":[50],"obtaining":[51],"particularly":[53],"clear":[54],"decomposition":[55,83],"theorem":[56],"special":[59],"case":[60],"where":[61],"has":[63,69],"no":[64,70],"isolated":[65],"vertices.":[66],"vertices":[71,106],"type":[74],"call":[76],"dominated":[77],"then":[78,110],"give":[80],"semi-direct":[82],"into":[87],"subgroup":[89,96],"locally":[91],"conjugating":[92],"automorphisms":[93],"by":[94],"stabilizing":[97],"certain":[99],"lattice":[100],"\"admissible":[102],"subsets\"":[103],"C.":[108],"characterize":[111],"those":[112],"graphs":[113],"for":[114],"which":[115],"product":[120],"(not":[121],"necessarily":[122],"semi-direct)":[123],"two":[125],"such":[126],"subgroups.":[127]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
