{"id":"https://openalex.org/W2811500773","doi":"https://doi.org/10.37236/4983","title":"On the Isomorphism Problem for Cayley Graphs of Abelian Groups whose Sylow Subgroups are Elementary Abelian or Cyclic","display_name":"On the Isomorphism Problem for Cayley Graphs of Abelian Groups whose Sylow Subgroups are Elementary Abelian or Cyclic","publication_year":2018,"publication_date":"2018-06-22","ids":{"openalex":"https://openalex.org/W2811500773","doi":"https://doi.org/10.37236/4983","mag":"2811500773"},"language":"en","primary_location":{"id":"doi:10.37236/4983","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4983","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/4983","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045745266","display_name":"Ted Dobson","orcid":null},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Ted Dobson","raw_affiliation_strings":["FAMNIT and IAM\r\nUniversity of Primorska"],"affiliations":[{"raw_affiliation_string":"FAMNIT and IAM\r\nUniversity of Primorska","institution_ids":["https://openalex.org/I118905719"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045745266"],"corresponding_institution_ids":["https://openalex.org/I118905719"],"apc_list":null,"apc_paid":null,"fwci":2.6894,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.89013527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"2","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":0.9842000007629395,"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":0.9842000007629395,"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/T11797","display_name":"graph theory and CDMA systems","score":0.963699996471405,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9341999888420105,"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/sylow-theorems","display_name":"Sylow theorems","score":0.8643249273300171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.846343994140625},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7839779853820801},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7358986139297485},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6955875158309937},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.6176515817642212},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.5543340444564819},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.46735620498657227},{"id":"https://openalex.org/keywords/group-isomorphism","display_name":"Group isomorphism","score":0.45265334844589233},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4052050709724426},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3859212398529053},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.34288907051086426},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.2241920828819275},{"id":"https://openalex.org/keywords/inner-automorphism","display_name":"Inner automorphism","score":0.11252197623252869},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.06013438105583191},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.049848347902297974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.040772199630737305}],"concepts":[{"id":"https://openalex.org/C124535231","wikidata":"https://www.wikidata.org/wiki/Q1057919","display_name":"Sylow theorems","level":4,"score":0.8643249273300171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.846343994140625},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7839779853820801},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7358986139297485},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6955875158309937},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.6176515817642212},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5543340444564819},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.46735620498657227},{"id":"https://openalex.org/C155190451","wikidata":"https://www.wikidata.org/wiki/Q742064","display_name":"Group isomorphism","level":5,"score":0.45265334844589233},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4052050709724426},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3859212398529053},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.34288907051086426},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2241920828819275},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.11252197623252869},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.06013438105583191},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.049848347902297974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.040772199630737305},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4983","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4983","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:repozitorij.upr.si:IzpisGradiva.php?id=9674","is_oa":true,"landing_page_url":"https://repozitorij.upr.si/IzpisGradiva.php?id=9674","pdf_url":null,"source":{"id":"https://openalex.org/S4377196486","display_name":"Repository of the University of Primorsk (University of Primorska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118905719","host_organization_name":"University of Primorska","host_organization_lineage":["https://openalex.org/I118905719"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 1077-8926","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.37236/4983","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4983","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2029460574","https://openalex.org/W2773448878","https://openalex.org/W2530902475","https://openalex.org/W2347437099","https://openalex.org/W2910524166","https://openalex.org/W2348282198","https://openalex.org/W4391053136","https://openalex.org/W1853074263","https://openalex.org/W2604556328","https://openalex.org/W1989359050"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,92],"if":[3,57,77,80],"certain":[4,64],"arithmetic":[5,65],"conditions":[6],"hold,":[7],"then":[8,67],"the":[9,28,44,49,55],"Cayley":[10,29,45,69],"isomorphism":[11,30,46],"problem":[12,31],"for":[13,32],"abelian":[14,23],"groups,":[15],"all":[16],"of":[17,41,52,71,88],"whose":[18],"Sylow":[19,34],"subgroups":[20],"are":[21,60,75,82,95],"elementary":[22],"or":[24],"cyclic,":[25],"reduces":[26],"to":[27,99],"its":[33],"subgroups.":[35],"This":[36],"yields":[37],"a":[38,85],"large":[39],"number":[40],"results":[42],"concerning":[43],"problem,":[47],"perhaps":[48],"most":[50],"interesting":[51],"which":[53],"is":[54],"following:":[56],"$p_1,\\ldots,":[58],"p_r$":[59],"distinct":[61],"primes":[62],"satisfying":[63],"conditions,":[66],"two":[68],"digraphs":[70],"$\\mathbb{Z}_{p_1}^{a_1}\\times\\cdots\\times\\mathbb{Z}_{p_r}^{a_r}$,":[72],"$a_i\\le":[73],"5$,":[74],"isomorphic":[76,83],"and":[78],"only":[79],"they":[81],"by":[84],"group":[86],"automorphism":[87],"$\\mathbb{Z}_{p_1}^{a_1}\\times\\cdots\\times\\mathbb{Z}_{p_r}^{a_r}$.":[89],"That":[90],"is,":[91],"such":[93],"groups":[94],"CI-groups":[96],"with":[97],"respect":[98],"digraphs.":[100]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}