{"id":"https://openalex.org/W2015910906","doi":"https://doi.org/10.1142/s021819670800441x","title":"CONSTRUCTING THE GROUP PRESERVING A SYSTEM OF FORMS","display_name":"CONSTRUCTING THE GROUP PRESERVING A SYSTEM OF FORMS","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2015910906","doi":"https://doi.org/10.1142/s021819670800441x","mag":"2015910906"},"language":"en","primary_location":{"id":"doi:10.1142/s021819670800441x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670800441x","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057832306","display_name":"Peter A. Brooksbank","orcid":"https://orcid.org/0000-0002-3985-2177"},"institutions":[{"id":"https://openalex.org/I131221577","display_name":"Bucknell University","ror":"https://ror.org/00fc1qt65","country_code":"US","type":"education","lineage":["https://openalex.org/I131221577"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"PETER A. BROOKSBANK","raw_affiliation_strings":["Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA","institution_ids":["https://openalex.org/I131221577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080046105","display_name":"E. A. O\u2019Brien","orcid":"https://orcid.org/0000-0001-9178-9040"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"E. A. O'BRIEN","raw_affiliation_strings":["Department of Mathematics, University of Auckland, Private Bag 92019, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Auckland, Private Bag 92019, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057832306"],"corresponding_institution_ids":["https://openalex.org/I131221577"],"apc_list":null,"apc_paid":null,"fwci":1.5413,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79208229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"02","first_page":"227","last_page":"241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983999729156494,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8616265654563904},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.7118557691574097},{"id":"https://openalex.org/keywords/general-linear-group","display_name":"General linear group","score":0.6459133625030518},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6245735287666321},{"id":"https://openalex.org/keywords/sesquilinear-form","display_name":"Sesquilinear form","score":0.6244491934776306},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.6207042336463928},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6036009788513184},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5443631410598755},{"id":"https://openalex.org/keywords/bilinear-map","display_name":"Bilinear map","score":0.45867735147476196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4482104480266571},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43427595496177673},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4296651780605316},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41109633445739746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32018786668777466},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.11284798383712769},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.101237952709198},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.0808006227016449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8616265654563904},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.7118557691574097},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.6459133625030518},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6245735287666321},{"id":"https://openalex.org/C163353815","wikidata":"https://www.wikidata.org/wiki/Q1931224","display_name":"Sesquilinear form","level":3,"score":0.6244491934776306},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.6207042336463928},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6036009788513184},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5443631410598755},{"id":"https://openalex.org/C142685569","wikidata":"https://www.wikidata.org/wiki/Q1086961","display_name":"Bilinear map","level":3,"score":0.45867735147476196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4482104480266571},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43427595496177673},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4296651780605316},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41109633445739746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32018786668777466},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.11284798383712769},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.101237952709198},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.0808006227016449},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":1,"locations":[{"id":"doi:10.1142/s021819670800441x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819670800441x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W618980177","https://openalex.org/W1530075677","https://openalex.org/W1970174797","https://openalex.org/W1976312168","https://openalex.org/W1976677460","https://openalex.org/W1998864653","https://openalex.org/W2006114752","https://openalex.org/W2015416631","https://openalex.org/W2039660064","https://openalex.org/W2042609201","https://openalex.org/W2068948309","https://openalex.org/W2071772182","https://openalex.org/W2091969516","https://openalex.org/W2118187131","https://openalex.org/W2120189374","https://openalex.org/W2317218640","https://openalex.org/W3105062562"],"related_works":["https://openalex.org/W2063684714","https://openalex.org/W2339851856","https://openalex.org/W126085529","https://openalex.org/W3071847929","https://openalex.org/W2015109384","https://openalex.org/W2015910906","https://openalex.org/W4237874256","https://openalex.org/W2923431995","https://openalex.org/W579189210","https://openalex.org/W48961076"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,16,24,29,47],"practical":[3],"algorithm":[4],"to":[5,36],"construct":[6,37],"the":[7,10,38,42],"subgroup":[8],"of":[9,18,44,46],"general":[11],"linear":[12],"group":[13,43],"that":[14],"preserves":[15],"system":[17],"bilinear":[19],"or":[20],"sesquilinear":[21],"forms":[22],"on":[23],"vector":[25],"space":[26],"defined":[27],"over":[28],"finite":[30],"field.":[31],"Components":[32],"include":[33],"efficient":[34],"algorithms":[35],"Jacobson":[39],"radical":[40],"and":[41],"units":[45],"matrix":[48],"algebra.":[49]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}