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Journal of Group Theory.
We say a group 𝐺 has property R ∞ R_{\infty} if the number R ( φ ) R(\varphi) of twisted conjugacy classes is infinite for every automorphism 𝜑 of 𝐺. For such groups, the R ∞ R_{\infty} -nilpotency degree is the least integer 𝑐 s