{"id":"https://openalex.org/W2014482702","doi":"https://doi.org/10.1145/2229163.2229176","title":"Testing nilpotence of galois groups in polynomial time","display_name":"Testing nilpotence of galois groups in polynomial time","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2014482702","doi":"https://doi.org/10.1145/2229163.2229176","mag":"2014482702"},"language":"en","primary_location":{"id":"doi:10.1145/2229163.2229176","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229176","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5003212467","display_name":"V. Arvind","orcid":"https://orcid.org/0000-0002-1988-7866"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"V. Arvind","raw_affiliation_strings":["Institute of Mathematical Sciences, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090691108","display_name":"Piyush P. Kurur","orcid":null},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Piyush P. Kurur","raw_affiliation_strings":["Indian Institute of Technology, Kanpur, India","Indian Institute of Technology , Kanpur , India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]},{"raw_affiliation_string":"Indian Institute of Technology , Kanpur , India","institution_ids":["https://openalex.org/I94234084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003212467"],"corresponding_institution_ids":["https://openalex.org/I59611059"],"apc_list":null,"apc_paid":null,"fwci":0.4281,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.70921002,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"3","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T10237","display_name":"Cryptography and Data Security","score":0.9991000294685364,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.8286065459251404},{"id":"https://openalex.org/keywords/generic-polynomial","display_name":"Generic polynomial","score":0.8019167184829712},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.7456724643707275},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5568992495536804},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5317555665969849},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5174675583839417},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4674696922302246},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.45232093334198},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.44525909423828125},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.4437717795372009},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44204461574554443},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.42710080742836},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4205903112888336},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.3777804970741272},{"id":"https://openalex.org/keywords/splitting-of-prime-ideals-in-galois-extensions","display_name":"Splitting of prime ideals in Galois extensions","score":0.2960141599178314},{"id":"https://openalex.org/keywords/galois-cohomology","display_name":"Galois cohomology","score":0.283199667930603},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04839026927947998}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8286065459251404},{"id":"https://openalex.org/C123450019","wikidata":"https://www.wikidata.org/wiki/Q5532677","display_name":"Generic polynomial","level":5,"score":0.8019167184829712},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.7456724643707275},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5568992495536804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5317555665969849},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5174675583839417},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4674696922302246},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.45232093334198},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.44525909423828125},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.4437717795372009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44204461574554443},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.42710080742836},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4205903112888336},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3777804970741272},{"id":"https://openalex.org/C194601146","wikidata":"https://www.wikidata.org/wiki/Q3042809","display_name":"Splitting of prime ideals in Galois extensions","level":4,"score":0.2960141599178314},{"id":"https://openalex.org/C182349385","wikidata":"https://www.wikidata.org/wiki/Q382839","display_name":"Galois cohomology","level":3,"score":0.283199667930603},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04839026927947998},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2229163.2229176","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229176","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1491399033","https://openalex.org/W1496801598","https://openalex.org/W1618309400","https://openalex.org/W1846067859","https://openalex.org/W1974672137","https://openalex.org/W1976456789","https://openalex.org/W1986905837","https://openalex.org/W1993524657","https://openalex.org/W1996266453","https://openalex.org/W2003536029","https://openalex.org/W2003573719","https://openalex.org/W2020601656","https://openalex.org/W2040858746","https://openalex.org/W2044116850","https://openalex.org/W2051170661","https://openalex.org/W2065800794","https://openalex.org/W2080980486","https://openalex.org/W2087869270","https://openalex.org/W2133406104","https://openalex.org/W2141040012","https://openalex.org/W2247589135","https://openalex.org/W2396266074","https://openalex.org/W7009886422"],"related_works":["https://openalex.org/W2064989766","https://openalex.org/W148891984","https://openalex.org/W2110869895","https://openalex.org/W1543706171","https://openalex.org/W2950252413","https://openalex.org/W2019990657","https://openalex.org/W2070655732","https://openalex.org/W1560173453","https://openalex.org/W2014482702","https://openalex.org/W2389261278"],"abstract_inverted_index":{"We":[0],"give":[1,56],"the":[2,9,29,41,44,49,106],"first":[3],"polynomial-time":[4,59],"algorithm":[5,34,60],"for":[6,81],"checking":[7],"whether":[8],"Galois":[10,78,102],"group":[11,103],"Gal(":[12,88,111],"f":[13,19,47,52,68,89,112],")":[14,22,71],"of":[15,32,43,46,51,86,104,110],"an":[16],"input":[17,65],"polynomial":[18,39,67,92],"(":[20,69,95],"X":[21,25,70,74,96,99],"\u2208":[23,72],"Q[":[24,73,98],"]":[26,75,100],"is":[27,35,105],"nilpotent:":[28],"running":[30],"time":[31],"our":[33],"bounded":[36],"by":[37],"a":[38,57,66,91],"in":[40],"size":[42],"coefficients":[45],"and":[48],"degree":[50],".":[53],"Additionally,":[54],"we":[55],"deterministic":[58],"that,":[61],"when":[62],"given":[63],"as":[64],"with":[76],"nilpotent":[77],"group,":[79],"computes":[80],"each":[82],"prime":[83],"factor":[84],"p":[85,94,107],"#":[87],"),":[90],"g":[93],")\u2208":[97],"whose":[101],"-Sylow":[108],"subgroup":[109],").":[113]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}