{"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}
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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.
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