{"id":"https://openalex.org/W2941351007","doi":null,"title":"The Klein Four-Group","display_name":"The Klein Four-Group","publication_year":2019,"publication_date":"2019-03-01","ids":{"openalex":"https://openalex.org/W2941351007","mag":"2941351007"},"language":"en","primary_location":{"id":"mag:2941351007","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/1903.0367v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"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/A5034819929","display_name":"Volker Th\u00fcrey","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Volker Th\u00fcrey","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5034819929"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9951000213623047,"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":0.9951000213623047,"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":0.003599999938160181,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.00019999999494757503,"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/klein-four-group","display_name":"Klein four-group","score":0.9810000061988831},{"id":"https://openalex.org/keywords/group-theory","display_name":"group theory","score":0.9269999861717224},{"id":"https://openalex.org/keywords/finite-groups","display_name":"finite groups","score":0.640999972820282},{"id":"https://openalex.org/keywords/symmetry-groups","display_name":"symmetry groups","score":0.3779999911785126}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6290131211280823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4509654641151428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4331551790237427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4305887520313263},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09074234962463379}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2941351007","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/1903.0367v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null}],"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/W3203374555","https://openalex.org/W65470527","https://openalex.org/W4237171600","https://openalex.org/W2886171075","https://openalex.org/W2312376909","https://openalex.org/W2134281156","https://openalex.org/W359244051","https://openalex.org/W2006993742","https://openalex.org/W1991486282","https://openalex.org/W2912435173"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2019-05-03T00:00:00"}