{"id":"https://openalex.org/W7225409580","doi":"https://doi.org/10.1142/s0219498828501058","title":"On central automorphisms and inner automorphisms of MD -groups","display_name":"On central automorphisms and inner automorphisms of MD -groups","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225409580","doi":"https://doi.org/10.1142/s0219498828501058"},"language":"en","primary_location":{"id":"doi:10.1142/s0219498828501058","doi":"https://doi.org/10.1142/s0219498828501058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219498828501058","pdf_url":null,"source":{"id":"https://openalex.org/S158116049","display_name":"Journal of Algebra and Its Applications","issn_l":"0219-4988","issn":["0219-4988","1793-6829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"Journal of Algebra and Its Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5133024015","display_name":"Tao Xu","orcid":"https://orcid.org/0000-0002-3043-8615","observed_orcids":["https://orcid.org/0000-0002-3043-8615"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao Xu","raw_affiliation_strings":["https://orcid.org/0000-0002-3043-8615"],"raw_orcid":"https://orcid.org/0000-0002-3043-8615","affiliations":[{"raw_affiliation_string":"https://orcid.org/0000-0002-3043-8615","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5160998983","display_name":"Heguo Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heguo Liu","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10849","display_name":"Finite Group Theory Research","score":0.9937000274658203,"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":0.9937000274658203,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0031999999191612005,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.0013000000035390258,"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/central-automorphisms","display_name":"central automorphisms","score":0.9879999756813049},{"id":"https://openalex.org/keywords/inner-automorphism-group","display_name":"inner automorphism group","score":0.9409999847412109},{"id":"https://openalex.org/keywords/finite-rank-groups","display_name":"finite rank groups","score":0.8769999742507935},{"id":"https://openalex.org/keywords/center-of-a-group","display_name":"center of a group","score":0.5709999799728394},{"id":"https://openalex.org/keywords/group-characterization","display_name":"characterization of groups","score":0.5509999990463257}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.9125999808311462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9047999978065491},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7303000092506409},{"id":"https://openalex.org/C162619202","wikidata":"https://www.wikidata.org/wiki/Q4826703","display_name":"Automorphisms of the symmetric and alternating groups","level":3,"score":0.5974000096321106},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5507000088691711},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5110999941825867},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4878999888896942},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.47269999980926514},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.4327000081539154},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.390500009059906},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.3643999993801117},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.35839998722076416},{"id":"https://openalex.org/C160826032","wikidata":"https://www.wikidata.org/wiki/Q286972","display_name":"p-group","level":3,"score":0.3357999920845032},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28450000286102295},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219498828501058","doi":"https://doi.org/10.1142/s0219498828501058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219498828501058","pdf_url":null,"source":{"id":"https://openalex.org/S158116049","display_name":"Journal of Algebra and Its Applications","issn_l":"0219-4988","issn":["0219-4988","1793-6829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"Journal of Algebra and Its Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2588561997","https://openalex.org/W2139859447","https://openalex.org/W2725225619","https://openalex.org/W1982233565","https://openalex.org/W3031901814","https://openalex.org/W3015241754","https://openalex.org/W2011888291","https://openalex.org/W2734670292","https://openalex.org/W2746308706","https://openalex.org/W4416399673"],"abstract_inverted_index":{"A":[0],"group":[1,30,54,57],"[Formula:":[2,11,20,43,47,63,69,77,80,85],"see":[3,12,21,44,48,64,70,78,81,86],"text]":[4,22,45,49,65,71,82],"with":[5,31],"finite":[6],"rank":[7],"is":[8,23],"called":[9],"an":[10,28],"text]-group":[13],"if":[14],"every":[15],"upper":[16],"central":[17,60],"factor":[18],"of":[19,27,58,62],"a":[24,38],"direct":[25],"product":[26],"abelian":[29,40],"the":[32,51,56,67],"maximal":[33],"condition":[34],"on":[35],"subgroups":[36],"and":[37,46,55],"divisible":[39],"group.":[41],"Let":[42],"be":[50],"inner":[52],"automorphism":[53],"all":[59,76],"automorphisms":[61],"fixing":[66],"center":[68],"elementwise,":[72],"respectively.":[73],"We":[74],"characterize":[75],"text]-groups":[79],"for":[83],"which":[84],"text].":[87]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}