{"title":"在阿贝尔群上具有一般乘传递作用的有限Morley秩群","authors":"A. Berkman, A. Borovik","doi":"10.2140/mt.2022.1.1","DOIUrl":null,"url":null,"abstract":"We investigate the configuration where a group of finite Morley rank acts definably and generically m -transitively on an elementary abelian p -group of Morley rank n , where p is an odd prime, and m ⩾ n . We conclude that m = n , and the action is equivalent to the natural action of GL n ( F ) on F n for some algebraically closed field F . This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Groups of finite Morley rank with a generically multiply transitive action on an abelian group\",\"authors\":\"A. Berkman, A. Borovik\",\"doi\":\"10.2140/mt.2022.1.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the configuration where a group of finite Morley rank acts definably and generically m -transitively on an elementary abelian p -group of Morley rank n , where p is an odd prime, and m ⩾ n . We conclude that m = n , and the action is equivalent to the natural action of GL n ( F ) on F n for some algebraically closed field F . This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.\",\"PeriodicalId\":21757,\"journal\":{\"name\":\"Simul. Model. Pract. Theory\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Simul. Model. Pract. Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/mt.2022.1.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Simul. Model. Pract. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/mt.2022.1.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
我们研究了这样的配置，其中有限Morley秩的组可定义地和一般地m -传递作用于Morley秩n的初等阿贝儿p -群，其中p是奇数素数，并且m大于或等于n。我们得出m = n的结论，并且对于某些代数闭场F，其作用等价于GL n (F)对F n的自然作用。这加强了我们早期的一个结果，并部分回答了Borovik和Cherlin在2008年提出的两个问题。
Groups of finite Morley rank with a generically multiply transitive action on an abelian group
We investigate the configuration where a group of finite Morley rank acts definably and generically m -transitively on an elementary abelian p -group of Morley rank n , where p is an odd prime, and m ⩾ n . We conclude that m = n , and the action is equivalent to the natural action of GL n ( F ) on F n for some algebraically closed field F . This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.
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