在阿贝尔群上具有一般乘传递作用的有限Morley秩群

Simul. Model. Pract. Theory Pub Date : 2021-07-21 DOI:10.2140/mt.2022.1.1

A. Berkman, A. Borovik

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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。

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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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Simul. Model. Pract. Theory

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