论文标题
有限的小组行动对有限莫利等级的亚伯群
Finite group actions on abelian groups of finite Morley rank
论文作者
论文摘要
本文关于有限的莫利等级类别（无限）阿贝尔群体的有限群体的行动开发了一些一般结果。它们与[16]中讨论的有限摩尔利等级的一系列问题有关。至关重要的是，AyşeBerkman和我本人即将进行的工作需要这些结果[5]，我们从[4]中删除了“清晰度”的假设。此外，他们提供了简单的代数群体对基本Abelian $ p $ - 有限摩尔利等级的简单代数群体的不可约束作用的长期猜想的证明[16，猜想12]。
This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially, these results are needed for the forthcoming work by Ayşe Berkman and myself [5] where we remove the `sharpness' assumption from [4]. Also, they yield a proof of the long standing conjecture of linearity of irreducible definable actions of simple algebraic groups on elementary abelian $p$-groups of finite Morley rank [16, Conjecture 12].
