{"id":"https://openalex.org/W1982348927","doi":"https://doi.org/10.1142/s0218196706003037","title":"ON GENERATION OF WREATH PRODUCTS OF CYCLIC GROUPS BY TWO STATE TIME VARYING MEALY AUTOMATA","display_name":"ON GENERATION OF WREATH PRODUCTS OF CYCLIC GROUPS BY TWO STATE TIME VARYING MEALY AUTOMATA","publication_year":2006,"publication_date":"2006-04-01","ids":{"openalex":"https://openalex.org/W1982348927","doi":"https://doi.org/10.1142/s0218196706003037","mag":"1982348927"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196706003037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003037","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/A5048986684","display_name":"Adam Woryna","orcid":"https://orcid.org/0000-0002-3463-7603"},"institutions":[{"id":"https://openalex.org/I119004910","display_name":"Silesian University of Technology","ror":"https://ror.org/02dyjk442","country_code":"PL","type":"education","lineage":["https://openalex.org/I119004910"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"ADAM WORYNA","raw_affiliation_strings":["Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-101 Gliwice, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-101 Gliwice, Poland","institution_ids":["https://openalex.org/I119004910","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048986684"],"corresponding_institution_ids":["https://openalex.org/I119004910","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.08089304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"02","first_page":"397","last_page":"415"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9994999766349792,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9994999766349792,"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/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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/wreath-product","display_name":"Wreath product","score":0.928398072719574},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8811391592025757},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.755490779876709},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.6131863594055176},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.5879527926445007},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5557364225387573},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5261477828025818},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5117282867431641},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5070936679840088},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.49069392681121826},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.4686274826526642},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4636474847793579},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.46036115288734436},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.4335523545742035},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3849424123764038},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3683014214038849},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10107210278511047},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.0754823088645935},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.07461300492286682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06642380356788635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05716696381568909},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.047958970069885254}],"concepts":[{"id":"https://openalex.org/C95635736","wikidata":"https://www.wikidata.org/wiki/Q1786640","display_name":"Wreath product","level":3,"score":0.928398072719574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8811391592025757},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.755490779876709},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.6131863594055176},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.5879527926445007},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5557364225387573},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5261477828025818},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5117282867431641},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5070936679840088},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.49069392681121826},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.4686274826526642},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4636474847793579},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.46036115288734436},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.4335523545742035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3849424123764038},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3683014214038849},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10107210278511047},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.0754823088645935},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.07461300492286682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06642380356788635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05716696381568909},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.047958970069885254},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196706003037","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003037","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Zero hunger","id":"https://metadata.un.org/sdg/2","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W29787842","https://openalex.org/W319884268","https://openalex.org/W416149594","https://openalex.org/W843129101","https://openalex.org/W1566117369","https://openalex.org/W1581663038","https://openalex.org/W1984237285","https://openalex.org/W2008356821","https://openalex.org/W2029477128","https://openalex.org/W2042740070","https://openalex.org/W2059810545","https://openalex.org/W2060903394","https://openalex.org/W2067889523","https://openalex.org/W2073707970","https://openalex.org/W2108389326","https://openalex.org/W2148609756","https://openalex.org/W2293859550","https://openalex.org/W2312204951","https://openalex.org/W2798943694","https://openalex.org/W4234295943","https://openalex.org/W4246912661","https://openalex.org/W4291439952","https://openalex.org/W4313152393"],"related_works":["https://openalex.org/W1973077274","https://openalex.org/W2963402871","https://openalex.org/W3119579515","https://openalex.org/W4287027350","https://openalex.org/W2110610939","https://openalex.org/W2963351346","https://openalex.org/W3191393695","https://openalex.org/W1995408789","https://openalex.org/W1982348927","https://openalex.org/W2155653874"],"abstract_inverted_index":{"We":[0,43],"proof":[1],"that":[2],"an":[3],"infinitely":[4],"iterated":[5],"wreath":[6],"product":[7],"of":[8,12,47],"finite":[9],"cyclic":[10],"groups":[11],"pairwise":[13],"coprime":[14],"orders":[15],"is":[16],"generated":[17],"as":[18],"a":[19,25,38],"topological":[20],"group":[21,29],"by":[22,37],"two":[23],"elements":[24],"and":[26],"b.":[27],"The":[28],"G":[30],"=":[31],"\u3008a,":[32],"b\u3009":[33],"may":[34],"be":[35],"represented":[36],"2-state":[39],"time-varying":[40],"Mealy":[41],"automaton.":[42],"derive":[44],"some":[45],"properties":[46],"G.":[48]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}