{"id":"https://openalex.org/W2019603599","doi":"https://doi.org/10.1080/10586458.2005.10128918","title":"Constructing Invariants for Finite Groups","display_name":"Constructing Invariants for Finite Groups","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2019603599","doi":"https://doi.org/10.1080/10586458.2005.10128918","mag":"2019603599"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2005.10128918","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128918","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5016942322","display_name":"Wilhelm Plesken","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. Plesken","raw_affiliation_strings":["Lehrstuhl B f\u00fcr Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl B f\u00fcr Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048450491","display_name":"Daniel Robertz","orcid":"https://orcid.org/0000-0003-1179-0012"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Robertz","raw_affiliation_strings":["Lehrstuhl B f\u00fcr Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl B f\u00fcr Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016942322"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.5565,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61453397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"2","first_page":"175","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9984999895095825,"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":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8476511240005493},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.7222058773040771},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6045469045639038},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"Invariant theory","score":0.6002402901649475},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5595725774765015},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.4879150092601776},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45756015181541443},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.44198721647262573},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3806505799293518},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33753612637519836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10987016558647156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8476511240005493},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.7222058773040771},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6045469045639038},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.6002402901649475},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5595725774765015},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.4879150092601776},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45756015181541443},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.44198721647262573},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3806505799293518},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33753612637519836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10987016558647156},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2005.10128918","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128918","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1128100130","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1128100130","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:publications.rwth-aachen.de:155605","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-033942%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Experimental mathematics 14(2), 175-188 (2005). doi:10.1080/10586458.2005.10128918","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W644150847","https://openalex.org/W1552996597","https://openalex.org/W1569582035","https://openalex.org/W1587264501","https://openalex.org/W1589940326","https://openalex.org/W1976677460","https://openalex.org/W1984446217","https://openalex.org/W2037956129","https://openalex.org/W2051046060","https://openalex.org/W2088338107","https://openalex.org/W2089793017","https://openalex.org/W2158309140"],"related_works":["https://openalex.org/W2584882758","https://openalex.org/W2126737417","https://openalex.org/W1524935011","https://openalex.org/W2525376760","https://openalex.org/W1566337467","https://openalex.org/W2019603599","https://openalex.org/W2963202524","https://openalex.org/W2370444048","https://openalex.org/W2972681526","https://openalex.org/W1976114908"],"abstract_inverted_index":{"It":[0,85],"is":[1,134,168,239,244],"well":[2],"known":[3],"that":[4,59],"the":[5,21,37,57,68,91,106,117,127,138,159,178,189,201,223,227,241],"ring":[6,69,92,128],"of":[7,10,39,70,93,108,120,129,140,161,203,206,230,232],"polynomial":[8,122,130],"invariants":[9,71,94,167,205],"a":[11,42,82,96,101,181,185],"finite":[12],"matrix":[13],"group":[14,179],"G":[15,79],"becomes":[16],"more":[17,19,219],"and":[18,33,143,184,247],"messy":[20],"further":[22],"one":[23,66,73,113,133,146],"moves":[24],"away":[25],"from":[26],"groups":[27],"generated":[28],"by":[29,99],"pseudoreflections,":[30],"see":[31],"[Huffman":[32],"Sloane":[34],"79].":[35],"Also,":[36],"number":[38,160],"generators":[40,162,221],"has":[41],"tendency":[43],"to":[44,53,89,136,164,197,216,235,267],"become":[45],"large.":[46],"In":[47,105,226],"this":[48,237,269],"experimental":[49],"study,":[50],"we":[51],"try":[52],"create":[54,165],"evidence":[55],"for":[56,211],"observation":[58],"these":[60,156],"unpleasant":[61],"properties":[62],"might":[63,80,114,264],"improve":[64],"if":[65,177],"enlarges":[67],"in":[72,222],"way":[74],"or":[75],"another.":[76],"For":[77],"instance,":[78,212],"fix":[81],"symplectic":[83,111,186],"form.":[84],"can":[86,147,213],"be":[87,214],"used":[88,215],"turn":[90],"into":[95,153],"Lie":[97,118,144],"algebra":[98,119],"introducing":[100],"G-invariant":[102,150],"Poisson":[103],"bracket.":[104],"absence":[107],"an":[109,198,249],"invariant":[110,121],"form,":[112],"still":[115],"consider":[116],"vector":[123],"fields":[124,231],"simultaneously":[125],"with":[126,257],"invariants.":[131],"If":[132],"prepared":[135],"leave":[137],"realm":[139],"commutative":[141],"rings":[142],"algebras,":[145],"also":[148,265],"take":[149],"differential":[151],"operators":[152],"account.":[154],"Under":[155],"additional":[157],"operations":[158],"necessary":[163],"all":[166],"often":[169],"drastically":[170],"decreased.":[171],"A":[172],"particularly":[173],"nice":[174],"situation":[175,229],"arises":[176],"fixes":[180],"quadratic":[182],"form":[183,187],"at":[188],"same":[190],"time,":[191],"because":[192],"together":[193],"they":[194],"give":[195],"rise":[196],"endomorphism":[199],"on":[200],"space":[202],"homogeneous":[204],"any":[207],"given":[208],"degree":[209],"that,":[210],"single":[217],"out":[218],"effective":[220],"new":[224],"sense.":[225],"classical":[228],"characteristic":[233],"zero,":[234],"which":[236],"paper":[238],"restricted,":[240],"averaging":[242],"operator":[243],"both":[245],"theoretically":[246],"algorithmically":[248],"important":[250],"tool,":[251],"whose":[252],"computational":[253],"feasibility,":[254],"however,":[255],"decreases":[256],"increasing":[258],"degrees.":[259],"The":[260],"methods":[261],"presented":[262],"here":[263],"help":[266],"avoid":[268],"difficulty.":[270]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
