{"id":"https://openalex.org/W1963650429","doi":"https://doi.org/10.1142/s0218196700000145","title":"THE POWER OF THE GROUP-IDENTITIES FOR ITERATION","display_name":"THE POWER OF THE GROUP-IDENTITIES FOR ITERATION","publication_year":2000,"publication_date":"2000-06-01","ids":{"openalex":"https://openalex.org/W1963650429","doi":"https://doi.org/10.1142/s0218196700000145","mag":"1963650429"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196700000145","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196700000145","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Z. \u00c9SIK","raw_affiliation_strings":["Department of Computer Science, Szeged, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Szeged, Hungary","institution_ids":["https://openalex.org/I227486990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017293831"],"corresponding_institution_ids":["https://openalex.org/I227486990"],"apc_list":null,"apc_paid":null,"fwci":0.5259,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75307465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"10","issue":"03","first_page":"349","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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/T10142","display_name":"Formal Methods in Verification","score":0.9979000091552734,"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/T11567","display_name":"semigroups and automata theory","score":0.996399998664856,"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":0.8518826961517334},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.7547497749328613},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7519515752792358},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7224059700965881},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6638166904449463},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5523074269294739},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5072750449180603},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.506625235080719},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3304526209831238},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2926274836063385},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.06157448887825012},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.054026782512664795}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8518826961517334},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.7547497749328613},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7519515752792358},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7224059700965881},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6638166904449463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5523074269294739},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5072750449180603},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.506625235080719},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3304526209831238},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2926274836063385},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.06157448887825012},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.054026782512664795},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196700000145","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196700000145","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:pure.atira.dk:publications/5c285810-8092-11db-8b97-000ea68e967b","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/5c285810-8092-11db-8b97-000ea68e967b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Esik, Z 2000, 'The Power of the Group Identities for Iteration', International Journal of Algebra and Computation, vol. 10, no. 3, pp. 349-373.","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W124288489","https://openalex.org/W137476671","https://openalex.org/W1973730262","https://openalex.org/W1975977228","https://openalex.org/W1979971526","https://openalex.org/W2026410426","https://openalex.org/W2043871010","https://openalex.org/W2044747903","https://openalex.org/W2091780332","https://openalex.org/W2107674601","https://openalex.org/W2123694805","https://openalex.org/W4232114544"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W2331020993","https://openalex.org/W4383764068","https://openalex.org/W1481826604","https://openalex.org/W1797057780","https://openalex.org/W1501430220","https://openalex.org/W3187762542","https://openalex.org/W1587864502","https://openalex.org/W2404739533","https://openalex.org/W255137432"],"abstract_inverted_index":{"It":[0,76],"has":[1],"been":[2],"shown":[3],"that":[4,78],"the":[5,11,29,33,37,58,62,66,74,80,85,89],"axioms":[6],"of":[7,14,49,57,73,88],"iteration":[8,15],"theories":[9,25,60],"capture":[10],"equational":[12,86],"properties":[13],"in":[16,61],"several":[17],"different":[18],"models":[19],"related":[20],"to":[21,36],"computer":[22],"science.":[23],"Iteration":[24],"are":[26,82],"axiomatizable":[27],"by":[28,52,65],"Conway":[30,67],"identities":[31,51,68],"and":[32,69],"group-identities":[34,81],"corresponding":[35],"finite":[38],"(simple)":[39],"groups.":[40],"In":[41],"this":[42],"paper":[43],"we":[44],"provide":[45],"a":[46,54],"complete":[47],"analysis":[48],"these":[50],"giving":[53],"concrete":[55],"description":[56],"free":[59],"variety":[63,90],"axiomatized":[64],"any":[70],"given":[71],"subcollection":[72],"group-identities.":[75],"follows":[77],"when":[79],"effectively":[83],"given,":[84],"theory":[87],"is":[91],"decidable.":[92]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}