{"title":"可接受组的定义字段","authors":"D. Neftin, U. Vishne","doi":"10.51286/albjm/1693956885","DOIUrl":null,"url":null,"abstract":"A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.","PeriodicalId":309211,"journal":{"name":"Albanian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FIELDS OF DEFINITION FOR ADMISSIBLE GROUPS\",\"authors\":\"D. Neftin, U. Vishne\",\"doi\":\"10.51286/albjm/1693956885\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.\",\"PeriodicalId\":309211,\"journal\":{\"name\":\"Albanian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Albanian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.51286/albjm/1693956885\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Albanian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.51286/albjm/1693956885","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.
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