{"id":"https://openalex.org/W2138593475","doi":"https://doi.org/10.1142/s0219061315500099","title":"On model-theoretic connected components in some group extensions","display_name":"On model-theoretic connected components in some group extensions","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2138593475","doi":"https://doi.org/10.1142/s0219061315500099","mag":"2138593475"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061315500099","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061315500099","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"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":"Journal of Mathematical Logic","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/A5021547552","display_name":"Jakub Gismatullin","orcid":"https://orcid.org/0000-0002-4711-3075"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Gismatullin","raw_affiliation_strings":["Instytut Matematyczny Uniwersytetu Wroc\u0142awskiego, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny Uniwersytetu Wroc\u0142awskiego, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033122829","display_name":"Krzysztof Krupi\u0144ski","orcid":"https://orcid.org/0000-0002-2243-4411"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Krupi\u0144ski","raw_affiliation_strings":["Instytut Matematyczny Uniwersytetu Wroc\u0142awskiego, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny Uniwersytetu Wroc\u0142awskiego, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I219388962"],"apc_list":null,"apc_paid":null,"fwci":2.116,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86110297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"15","issue":"02","first_page":"1550009","last_page":"1550009"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9983000159263611,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9983000159263611,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9934999942779541,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.991599977016449,"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/mathematics","display_name":"Mathematics","score":0.8794655799865723},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7042882442474365},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6244044303894043},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5669965744018555},{"id":"https://openalex.org/keywords/covering-space","display_name":"Covering space","score":0.5287180542945862},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5047124624252319},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5046683549880981},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"Fundamental group","score":0.5035497546195984},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4885038137435913},{"id":"https://openalex.org/keywords/normal-subgroup","display_name":"Normal subgroup","score":0.4786854386329651},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4519972801208496},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.4197206497192383},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3871566355228424}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8794655799865723},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7042882442474365},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6244044303894043},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5669965744018555},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.5287180542945862},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5047124624252319},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5046683549880981},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.5035497546195984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4885038137435913},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.4786854386329651},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4519972801208496},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.4197206497192383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3871566355228424},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061315500099","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061315500099","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"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":"Journal of Mathematical Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W121143651","https://openalex.org/W193109478","https://openalex.org/W303679994","https://openalex.org/W1514814112","https://openalex.org/W1556069388","https://openalex.org/W1558005980","https://openalex.org/W1600092771","https://openalex.org/W1986913345","https://openalex.org/W1990678597","https://openalex.org/W2052389755","https://openalex.org/W2075604393","https://openalex.org/W2077901627","https://openalex.org/W2093835911","https://openalex.org/W2099705227","https://openalex.org/W2109047913","https://openalex.org/W2113874518","https://openalex.org/W2134988756","https://openalex.org/W2144642941","https://openalex.org/W2158457721","https://openalex.org/W2498676440","https://openalex.org/W2499758444","https://openalex.org/W2561618607","https://openalex.org/W2963559413","https://openalex.org/W3024042053","https://openalex.org/W3100318695","https://openalex.org/W3102648519","https://openalex.org/W4230443229","https://openalex.org/W4300937596"],"related_works":["https://openalex.org/W4290238838","https://openalex.org/W2078049079","https://openalex.org/W2963889787","https://openalex.org/W4298875588","https://openalex.org/W2952266720","https://openalex.org/W2963063346","https://openalex.org/W1966053047","https://openalex.org/W2581713289","https://openalex.org/W4297964200","https://openalex.org/W4287726574"],"abstract_inverted_index":{"We":[0,24,187],"analyze":[1],"model-theoretic":[2],"connected":[3,57],"components":[4],"in":[5,26,75,128],"extensions":[6,64,143],"of":[7,19,28,36,54,65,82,84,90,99,108,123,137,144,148,151,168,172,192,195,204,211],"a":[8,109,129,156,190],"given":[9],"group":[10,110],"by":[11,17,115,178,217],"abelian":[12],"groups":[13,66,85,146,150,164,167],"which":[14,208],"are":[15],"defined":[16],"means":[18],"2-cocycles":[20],"with":[21,68,111],"finite":[22],"image.":[23],"characterize,":[25],"terms":[27],"these":[29,55],"2-cocycles,":[30],"when":[31],"the":[32,37,42,52,95,104,120,193,218],"smallest":[33,43,87,96],"type-definable":[34,88],"subgroup":[35,89,98],"corresponding":[38],"extension":[39],"differs":[40,93],"from":[41,94],"invariant":[44,97],"subgroup.":[45],"In":[46],"some":[47,141],"situations,":[48],"we":[49,78,158],"also":[50,188],"describe":[51],"quotient":[53],"two":[56],"components.":[58],"Using":[59],"our":[60,212],"general":[61],"results":[62],"about":[63],"together":[67],"Matsumoto\u2013Moore":[69],"theory":[70],"or":[71,147],"various":[72,135],"quasi-characters":[73],"considered":[74],"bounded":[76,91,100],"cohomology,":[77],"obtain":[79,189],"new":[80],"classes":[81],"examples":[83,136],"whose":[86],"index":[92],"index.":[101],"This":[102],"includes":[103],"first":[105],"known":[106,220],"example":[107,194],"this":[112,184],"property":[113],"found":[114],"Conversano":[116,196],"and":[117,165,197],"Pillay,":[118],"namely":[119],"universal":[121],"cover":[122],"[Formula:":[124,174,200,205],"see":[125,175,201,206],"text]":[126,202],"(interpreted":[127],"monster":[130],"model),":[131],"as":[132,134],"well":[133],"different":[138],"nature,":[139],"e.g.":[140],"central":[142],"free":[145,163],"fundamental":[149,166],"closed":[152,169],"orientable":[153,170],"surfaces.":[154],"As":[155],"corollary,":[157],"get":[159],"that":[160],"both":[161],"non-abelian":[162],"surfaces":[171],"genus":[173],"text],":[176,207],"expanded":[177],"predicates":[179],"for":[180,199],"all":[181],"subsets,":[182],"have":[183],"property,":[185],"too.":[186],"variant":[191],"Pillay":[198],"instead":[203],"(as":[209],"most":[210],"examples)":[213],"was":[214],"not":[215],"accessible":[216],"previously":[219],"methods.":[221]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}