Let G be a group and φ be an automorphism of G. Two elements x,y ∈ G are said to be φ-twisted conjugate if y = gxφ(g)−1 for some g ∈ G. We say that a group G has the R∞-property if the number of φ-twisted conjugacy classes is infinite for every automorphism φ of G. In this paper, we prove that twisted Chevalley groups over a field k of characteristic zero have the R∞-property as well as the S∞-property if k has finite transcendence degree over ℚ or Aut(k) is periodic.

中文翻译：

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扭曲的 Chevalley 群中的扭曲共轭类

让G成为一个群体并且φ是的自同构G. 两个元素X,是的 ∈ G据说是φ- 扭曲共轭 if是的 = GXφ(G)-1对于一些G ∈ G. 我们说一组G有R∞- 属性，如果数量φ-对于每个自同构，扭曲的共轭类是无限的φ的G. 在本文中，我们证明了扭曲的 Chevalley 群在一个域上ķ零特征具有R∞- 财产以及小号∞- 属性如果ķ具有有限超越度ℚ要么自动(ķ)是周期性的。