Recall that a pure F-structure is a kind of generalized torus action. The main result asserts that if a compact positively curved manifold M" admits an invariant pure F-structure such that each orbit has positive dimension, then the fundamental group has a finite cyclic subgroup with index less than wn, a constant depending only on n. As an application, we conclude that for all 0 < 6 g 1, the fundamental group of a ^-pinched n-manifold either has a cyclic subgroup with index less than wn or has order less.than w(?,<5), a constant depending only on n and i5. In particular, this substantially improves the main result in [Rol].
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机译：回想一下，纯F结构是一种广义的环面作用。主要结果断言，如果紧实的正弯曲流形M“接纳不变的纯F结构，使得每个轨道具有正维，则基本组具有索引小于wn的有限循环子组，该常数仅取决于n。作为一个应用，我们得出结论，对于所有0 <6 g 1，^收缩n流形的基本基团具有索引小于wn的循环子群或具有小于w（？，<5）的阶。仅取决于n和i5的常数，特别是，这实质上改善了[Rol]中的主要结果。
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