{"id":"https://openalex.org/W4235060053","doi":"https://doi.org/10.1201/9780429332401-3","title":"Groups","display_name":"Groups","publication_year":2021,"publication_date":"2021-01-12","ids":{"openalex":"https://openalex.org/W4235060053","doi":"https://doi.org/10.1201/9780429332401-3"},"language":"en","primary_location":{"id":"doi:10.1201/9780429332401-3","doi":"https://doi.org/10.1201/9780429332401-3","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9780429332401-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306463075","display_name":"CRC Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320584","host_organization_name":"CRC Press","host_organization_lineage":["https://openalex.org/P4310320584","https://openalex.org/P4310320547"],"host_organization_lineage_names":["CRC Press","Taylor & Francis"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"An Introduction to Groups","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W1556160186","display_name":"An Introduction to Groups"},"type":"book-chapter","is_traditional":true,"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/A5076385150","display_name":"David Asche","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David Asche","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5076385150"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"14","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.7109000086784363,"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":0.7109000086784363,"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/T12504","display_name":"Mathematics and Applications","score":0.20960000157356262,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.011800000444054604,"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/groups","display_name":"groups","score":0.8349999785423279},{"id":"https://openalex.org/keywords/group-axioms","display_name":"group axioms","score":0.949999988079071},{"id":"https://openalex.org/keywords/binary-operations","display_name":"binary operations","score":0.7590000033378601},{"id":"https://openalex.org/keywords/subgroups","display_name":"subgroups","score":0.859000027179718},{"id":"https://openalex.org/keywords/abstract-algebra","display_name":"abstract algebra","score":0.5920000076293945},{"id":"https://openalex.org/keywords/group-theory","display_name":"group theory","score":0.6000000238418579}],"concepts":[{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.31562474370002747}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1201/9780429332401-3","doi":"https://doi.org/10.1201/9780429332401-3","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9780429332401-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306463075","display_name":"CRC Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320584","host_organization_name":"CRC Press","host_organization_lineage":["https://openalex.org/P4310320584","https://openalex.org/P4310320547"],"host_organization_lineage_names":["CRC Press","Taylor & Francis"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"An Introduction to Groups","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4242617691","https://openalex.org/W4238468341","https://openalex.org/W3176137474","https://openalex.org/W32881802","https://openalex.org/W4245030723","https://openalex.org/W7077493034","https://openalex.org/W3021175627","https://openalex.org/W971911115","https://openalex.org/W4388257738","https://openalex.org/W7095069228"],"abstract_inverted_index":{"A":[0],"group":[1,13,26,94],"consists":[2],"of":[3,6,11,22,24,31,60,86,92],"a":[4,67,81,93],"set":[5],"objects":[7],"called":[8,38],"the":[9,12,25,32,39,113],"elements":[10,23],"together":[14],"with":[15,110],"an":[16],"operation":[17,35],"which":[18,50,69,83],"combines":[19],"each":[20],"pair":[21],"to":[27,97,112],"produce":[28],"another":[29],"element":[30],"group.":[33],"This":[34],"is":[36,84],"usually":[37],"product.":[40],"In":[41],"addition,":[42],"there":[43],"are":[44,118],"several":[45],"fundamental":[46],"properties":[47],"or":[48],"axioms":[49],"must":[51,76],"be":[52,98],"satisfied.":[53],"Groups":[54],"occur":[55],"in":[56,80,101,106],"many":[57],"different":[58],"branches":[59],"science":[61],"and":[62,74],"mathematics":[63],"so":[64],"authors":[65],"need":[66],"definition":[68],"embraces":[70],"all":[71],"possible":[72],"applications":[73],"they":[75,103],"develop":[77],"our":[78],"theory":[79],"way":[82],"independent":[85],"any":[87],"particular":[88],"context.":[89],"Some":[90],"subsets":[91,117],"turn":[95],"out":[96],"particularly":[99],"interesting":[100],"that":[102],"form":[104],"groups":[105],"their":[107],"own":[108],"right":[109],"respect":[111],"same":[114],"operation.":[115],"Such":[116],"known":[119],"as":[120],"subgroups.":[121]},"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2022-05-12T00:00:00"}
