{"id":"https://openalex.org/W2915428283","doi":"https://doi.org/10.6092/issn.1972-5787/8751","title":"Commutativity Theorems in Groups with Power-like Maps","display_name":"Commutativity Theorems in Groups with Power-like Maps","publication_year":2018,"publication_date":"2018-12-05","ids":{"openalex":"https://openalex.org/W2915428283","doi":"https://doi.org/10.6092/issn.1972-5787/8751","mag":"2915428283"},"language":"en","primary_location":{"id":"pmh:oai:doaj.org/article:bbeef9bafdfa4a7c9be4c67170a4b612","is_oa":true,"landing_page_url":"https://doaj.org/article/bbeef9bafdfa4a7c9be4c67170a4b612","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Formalized Reasoning, Vol 12, Iss 1, Pp 1-10 (2019)","raw_type":"article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/bbeef9bafdfa4a7c9be4c67170a4b612","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018968176","display_name":"R. Padmanabhan","orcid":null},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Padmanabhan, Ranganathan","raw_affiliation_strings":["Department of Mathematics, University of Manitoba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100354779","display_name":"Yang Zhang","orcid":"https://orcid.org/0000-0003-2085-337X"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhang, Yang","raw_affiliation_strings":["Department of Mathematics, University of Manitoba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I46247651"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30736498,"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":0.9945999979972839,"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":0.9945999979972839,"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":0.9916999936103821,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9866999983787537,"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/commutative-property","display_name":"Commutative property","score":0.5836486220359802},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5337202548980713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5185014009475708},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40323132276535034},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3400011658668518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11298170685768127}],"concepts":[{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5836486220359802},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5337202548980713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5185014009475708},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40323132276535034},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3400011658668518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11298170685768127},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:doaj.org/article:bbeef9bafdfa4a7c9be4c67170a4b612","is_oa":true,"landing_page_url":"https://doaj.org/article/bbeef9bafdfa4a7c9be4c67170a4b612","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Formalized Reasoning, Vol 12, Iss 1, Pp 1-10 (2019)","raw_type":"article"},{"id":"doi:10.6092/issn.1972-5787/8751","is_oa":true,"landing_page_url":"https://doi.org/10.6092/issn.1972-5787/8751","pdf_url":null,"source":{"id":"https://openalex.org/S7407050985","display_name":"Universit\u00e0 degli Studi di Bologna","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:bbeef9bafdfa4a7c9be4c67170a4b612","is_oa":true,"landing_page_url":"https://doaj.org/article/bbeef9bafdfa4a7c9be4c67170a4b612","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Formalized Reasoning, Vol 12, Iss 1, Pp 1-10 (2019)","raw_type":"article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1494059412","https://openalex.org/W2030592198","https://openalex.org/W2033513250","https://openalex.org/W2401228324","https://openalex.org/W2564246343","https://openalex.org/W2564543232","https://openalex.org/W2620840829"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"There":[0],"are":[1,72],"several":[2],"commutativity":[3],"theorems":[4,92],"in":[5,51,68],"groups":[6],"and":[7,48,110],"rings":[8],"which":[9,26],"involve":[10],"power":[11,94,105,129],"maps":[12,106],"f(x)":[13,107],"=":[14,35,108],"xn.":[15],"The":[16],"most":[17],"famous":[18],"example":[19],"of":[20,59,62,76,104,128,148],"this":[21],"kind":[22],"is":[23,37],"Jacobson's":[24],"theorem":[25],"asserts":[27],"that":[28],"any":[29,54,77],"ring":[30],"satisfying":[31],"the":[32,60,69,74,101,146],"identity":[33],"xn":[34,109],"x":[36],"commutative.":[38],"Such":[39],"statements":[40],"belong":[41],"to":[42,90,117],"first":[43],"order":[44],"logic":[45],"with":[46,120],"equality":[47],"hence":[49],"provable,":[50],"principle,":[52],"by":[53],"first-order":[55,78],"theorem-prover.":[56,79],"However,":[57],"because":[58],"presence":[61],"an":[63,86],"arbitrary":[64],"integer":[65,121],"parameter":[66],"n":[67],"exponent,":[70],"they":[71],"outside":[73],"scope":[75],"In":[80],"particular,":[81],"one":[82,113],"cannot":[83],"use":[84],"such":[85,149],"automated":[87],"reasoning":[88],"system":[89],"prove":[91],"involving":[93],"maps.":[95],"Here":[96],"we":[97,131],"focus":[98],"just":[99],"on":[100],"needed":[102],"properties":[103,127],"show":[111,132],"how":[112,133],"can":[114,136],"avoid":[115],"having":[116],"reason":[118],"explicitly":[119],"exponents.":[122],"Implementing":[123],"these":[124],"new":[125],"equational":[126],"maps,":[130],"a":[134,138],"theorem-prover":[135],"be":[137],"handy":[139],"tool":[140],"for":[141],"quickly":[142],"proving":[143],"or":[144],"confirming":[145],"truth":[147],"theorems.":[150]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}