Abstract A group G has the R ∞ {R_{\infty}} -property if the number R ⁢ ( φ ) {R(\varphi)} of twisted conjugacy classes is infinite for any automorphism φ of G. For such a group G, the R ∞ {R_{\infty}} -nilpotency degree is the least integer c such that G / γ c + 1 ⁢ ( G ) {G/\gamma_{c+1}(G)} still has the R ∞ {R_{\infty}} -property. In this paper, we determine the R ∞ {R_{\infty}} -nilpotency degree of all Baumslag–Solitar groups.

中文翻译：

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Baumslag-Solitar 群的幂零商的 𝑅∞-性质

摘要 如果 G 的任何自同构 φ 的扭曲共轭类的数目 R ⁢ ( φ ) {R(\varphi)} 是无限的，则群 G 具有 R ∞ {R_{\infty}} -性质。对于这样的群 G ，R ∞ {R_{\infty}} -nilpotency 度是最小整数 c，使得 G / γ c + 1 ⁢ ( G ) {G/\gamma_{c+1}(G)} 仍然具有 R ∞ {R_{\infty}} -属性。在本文中，我们确定了所有 Baumslag–Solitar 群的 R ∞ {R_{\infty}} -nilpotency 度。