可接受组的定义字段

Albanian Journal of Mathematics Pub Date : 2011-10-19 DOI:10.51286/albjm/1693956885

D. Neftin, U. Vishne

{"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}

引用次数: 0

摘要

如果有一个以M为中心的除法代数，且在M上有一个极大子域G-伽罗瓦，则有限群G在域M上是可容许的。我们考虑了M的子域K在M上可容许的九种可能的概念，其中在K上可以断言除法代数、极大子域或伽罗瓦群是有定义的。我们完全确定了所有变体之间的逻辑含义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

FIELDS OF DEFINITION FOR ADMISSIBLE GROUPS

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Albanian Journal of Mathematics

自引率

0.00%

发文量

期刊最新文献

On the Hilbert Function of Intersections of a Hypersurface with General Reducible Curves Explicit Zero-Free Regions and a $\tau$-Li-type Criterion FIELDS OF DEFINITION FOR ADMISSIBLE GROUPS On Gromov-Witten Theory of Toric Gerbes