{"id":"https://openalex.org/W2726287124","doi":"https://doi.org/10.1142/s0218196717500308","title":"On the Gruenberg\u2013Kegel graph of integral group rings of finite groups","display_name":"On the Gruenberg\u2013Kegel graph of integral group rings of finite groups","publication_year":2017,"publication_date":"2017-08-01","ids":{"openalex":"https://openalex.org/W2726287124","doi":"https://doi.org/10.1142/s0218196717500308","mag":"2726287124"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196717500308","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500308","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":true,"oa_status":"green","oa_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/15872/1/Reductionpaper.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021492268","display_name":"Wolfgang Kimmerle","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. Kimmerle","raw_affiliation_strings":["IGT, Fachbereich Mathematik, University of Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"IGT, Fachbereich Mathematik, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101451426","display_name":"Alexander Konovalov","orcid":"https://orcid.org/0000-0001-5299-3292"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. Konovalov","raw_affiliation_strings":["Centre for Interdisciplinary Research in Computational Algebra, University of St Andrews, St Andrews, Scotland, UK"],"affiliations":[{"raw_affiliation_string":"Centre for Interdisciplinary Research in Computational Algebra, University of St Andrews, St Andrews, Scotland, UK","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021492268"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":5.6034,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.96812081,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"06","first_page":"619","last_page":"631"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9799000024795532,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9542999863624573,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9164371490478516},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5566196441650391},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5035726428031921},{"id":"https://openalex.org/keywords/simple-group","display_name":"Simple group","score":0.45466935634613037},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4187206029891968},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.17023661732673645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9164371490478516},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5566196441650391},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5035726428031921},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.45466935634613037},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4187206029891968},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.17023661732673645},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196717500308","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500308","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:research-repository.st-andrews.ac.uk:10023/15872","is_oa":true,"landing_page_url":"https://hdl.handle.net/10023/15872","pdf_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/15872/1/Reductionpaper.pdf","source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:research-repository.st-andrews.ac.uk:10023/15872","is_oa":true,"landing_page_url":"https://hdl.handle.net/10023/15872","pdf_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/15872/1/Reductionpaper.pdf","source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G678811400","display_name":null,"funder_award_id":"EP/M022641/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2726287124.pdf","grobid_xml":"https://content.openalex.org/works/W2726287124.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W161973657","https://openalex.org/W1964362651","https://openalex.org/W1974549909","https://openalex.org/W1976524169","https://openalex.org/W2007301302","https://openalex.org/W2010708621","https://openalex.org/W2013829889","https://openalex.org/W2017694780","https://openalex.org/W2020531904","https://openalex.org/W2021784250","https://openalex.org/W2031415535","https://openalex.org/W2031821019","https://openalex.org/W2074595135","https://openalex.org/W2083442986","https://openalex.org/W2089386851","https://openalex.org/W3090719294","https://openalex.org/W3099760756","https://openalex.org/W4247456395"],"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":{"The":[0],"prime":[1,19,55,93],"graph":[2,8,20,56,86,94],"question":[3,57],"asks":[4],"whether":[5],"the":[6,18,22,35,54,84,92],"Gruenberg\u2013Kegel":[7,85],"of":[9,21,26,34,53,87,95],"an":[10],"integral":[11],"group":[12,25,36],"ring":[13],"[Formula:":[14,27,37,48,69,96],"see":[15,28,38,49,70,97],"text],":[16,29],"i.e.":[17],"normalized":[23],"unit":[24],"coincides":[30,90],"with":[31,91],"that":[32,83],"one":[33],"text].":[39,98],"In":[40],"this":[41,64],"note,":[42],"we":[43],"prove":[44],"for":[45],"finite":[46,67],"groups":[47,68,89],"text]":[50,71],"a":[51],"reduction":[52,65],"to":[58,66],"almost":[59],"simple":[60],"groups.":[61],"We":[62],"apply":[63],"whose":[72],"order":[73],"is":[74],"divisible":[75],"by":[76],"at":[77],"most":[78],"three":[79],"primes":[80],"and":[81],"show":[82],"such":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}