论文标题
在有限的Prüfer等级的残留有限群体中扭曲的共轭
Twisted conjugacy in residually finite groups of finite Prüfer rank
论文作者
论文摘要
假设，$ g $是有限的上级有限的剩余组，承认有限的reidemister $ r（φ）$（$φ$ twisted conjugacy类的数量）。我们证明，这种$ g $是逐项可溶的（换句话说，任何有限的上级有限的剩余群体（不是逐句的）都有$ r_ \ infty $属性）。 减少是本文第二个主要定理证明的第一步：假设，$ g $是有限的Prüfer等级的残留有限的组，而$φ$是其自动形态，$ r（φ）<\ infty $;那么$ r（φ）$等于$ g $的有限维度不可约的单一表示的等效类别的数量，它们是双映射的固定点$ \widehatφ：[ρ] \ mapsto [ρ\circcφ] $（即，我们证明了tbft $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _f $ _。组）。
Suppose, $G$ is a residually finite group of finite upper rank admitting an automorphism $φ$ with finite Reidemeister number $R(φ)$ (the number of $φ$-twisted conjugacy classes). We prove that such $G$ is soluble-by-finite (in other words, any residually finite group of finite upper rank, which is not soluble-by-finite, has the $R_\infty$ property). This reduction is the first step in the proof of the second main theorem of the paper: suppose, $G$ is a residually finite group of finite Prüfer rank and $φ$ is its automorphism with $R(φ)<\infty$; then $R(φ)$ is equal to the number of equivalence classes of finite-dimensional irreducible unitary representations of $G$, which are fixed points of the dual map $\widehatφ:[ρ]\mapsto [ρ\circ φ]$ (i.e., we prove the TBFT$_f$, the finite version of the conjecture about the twisted Burnside-Frobenius theorem, for such groups).
