{"id":"https://openalex.org/W4245789266","doi":"https://doi.org/10.2178/bsl/1186666149","title":"Describing Groups","display_name":"Describing Groups","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W4245789266","doi":"https://doi.org/10.2178/bsl/1186666149"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1186666149","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1186666149","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic 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/A5047690936","display_name":"Andr\u00e9 Nies","orcid":"https://orcid.org/0000-0002-0666-5180"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Andr\u00e9 Nies","raw_affiliation_strings":["Department of Computer Science, Auckland University, Auckland, New Zealand, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Auckland University, Auckland, New Zealand, E-mail:","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047690936"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":null,"apc_paid":null,"fwci":2.6175,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.90159393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"3","first_page":"305","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.709527850151062},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6150656938552856},{"id":"https://openalex.org/keywords/finitely-generated-group","display_name":"Finitely generated group","score":0.5968260765075684},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5370970964431763},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5152044892311096},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4743674695491791},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4622265100479126},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4558180868625641},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4444366693496704},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.43170586228370667},{"id":"https://openalex.org/keywords/stallings-theorem-about-ends-of-groups","display_name":"Stallings theorem about ends of groups","score":0.4150986671447754},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4084901213645935},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36673834919929504},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.3650737404823303},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3481101989746094},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3261982798576355},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15846356749534607},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0848923921585083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0606837272644043}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.709527850151062},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6150656938552856},{"id":"https://openalex.org/C2780811992","wikidata":"https://www.wikidata.org/wiki/Q21083858","display_name":"Finitely generated group","level":3,"score":0.5968260765075684},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5370970964431763},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5152044892311096},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4743674695491791},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4622265100479126},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4558180868625641},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4444366693496704},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.43170586228370667},{"id":"https://openalex.org/C58249144","wikidata":"https://www.wikidata.org/wiki/Q7597316","display_name":"Stallings theorem about ends of groups","level":3,"score":0.4150986671447754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4084901213645935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36673834919929504},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3650737404823303},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3481101989746094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3261982798576355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15846356749534607},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0848923921585083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0606837272644043},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/bsl/1186666149","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1186666149","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1186666149","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1186666149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:researchspace.auckland.ac.nz:2292/9656","is_oa":false,"landing_page_url":"http://hdl.handle.net/2292/9656","pdf_url":null,"source":{"id":"https://openalex.org/S7407055463","display_name":"ResearchSpace (University of Auckland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I154130895","host_organization_name":"University of Auckland","host_organization_lineage":["https://openalex.org/I154130895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W591591544","https://openalex.org/W1026721552","https://openalex.org/W1501737527","https://openalex.org/W1517606395","https://openalex.org/W1587860830","https://openalex.org/W1601654835","https://openalex.org/W1966217515","https://openalex.org/W1994584977","https://openalex.org/W2018748198","https://openalex.org/W2032074224","https://openalex.org/W2032868343","https://openalex.org/W2050667277","https://openalex.org/W2071077564","https://openalex.org/W2077908282","https://openalex.org/W2079152571","https://openalex.org/W2099848457","https://openalex.org/W2124807316","https://openalex.org/W2132750992","https://openalex.org/W2138252926","https://openalex.org/W2334373984","https://openalex.org/W4213285485","https://openalex.org/W4253601112","https://openalex.org/W6654865930","https://openalex.org/W6658309904","https://openalex.org/W6663447628","https://openalex.org/W6670056662","https://openalex.org/W6670317223"],"related_works":["https://openalex.org/W1590360997","https://openalex.org/W2952241151","https://openalex.org/W2087413461","https://openalex.org/W2963670976","https://openalex.org/W2771827938","https://openalex.org/W2051257621","https://openalex.org/W2101435336","https://openalex.org/W1981717402","https://openalex.org/W4205171319","https://openalex.org/W1154677386"],"abstract_inverted_index":{"Abstract":[0],"Two":[1],"ways":[2],"of":[3,34,61,80,86,103,111,120,142],"describing":[4],"a":[5,24,29,58,62,121,125,133],"group":[6,11,39,51,72,122],"are":[7],"considered.":[8],"1.":[9],"A":[10],"is":[12,52,57,73,124,135,146],"finite-automaton":[13],"presentable":[14],"if":[15,55,132],"its":[16],"elements":[17],"can":[18,41],"be":[19,42],"represented":[20],"by":[21,44],"strings":[22,36],"over":[23],"finite":[25,45],"alphabet,":[26],"in":[27,137],"such":[28],"way":[30],"that":[31,70,131],"the":[32,38,68,71,77,81,97,108,112,118,140],"set":[33],"representing":[35],"and":[37,114,148],"operation":[40],"recognized":[43],"automata.":[46],"2.":[47],"An":[48],"infinite":[49],"f.g.":[50],"quasi-finitely":[53,104,149],"axiomatizable":[54,105],"there":[56],"description":[59],"consisting":[60],"single":[63],"first-order":[64],"sentence,":[65],"together":[66],"with":[67,139],"information":[69],"finitely":[74],"generated.":[75],"In":[76,96],"first":[78],"part":[79],"paper":[82],"we":[83,100],"survey":[84],"examples":[85,102],"FA-presentable":[87],"groups,":[88,106],"but":[89],"also":[90,129],"discuss":[91],"theorems":[92],"restricting":[93],"this":[94],"class.":[95],"second":[98],"part,":[99],"give":[101],"consider":[107],"algebraic":[109],"content":[110],"notion,":[113],"compare":[115],"it":[116,145],"to":[117],"notion":[119],"which":[123],"prime":[126,147],"model.":[127],"We":[128],"show":[130],"structure":[134],"bi-interpretable":[136],"parameters":[138],"ring":[141],"integers,":[143],"then":[144],"axiomatizable.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-04T09:04:59.091469","created_date":"2022-05-12T00:00:00"}