论文标题
$ \ mathbb z^k $中的某些花圈产品中的reidemeister课程
Reidemeister classes in some wreath products by $\mathbb Z^k$
论文作者
论文摘要
在受限的花环产品中，$ g \ wr \ mathbb z^k $，其中$ g $是一个有限的阿贝尔集团，我们发现三个大型组，承认具有有限的reidemeister $ r（φ）$的$ reidemister $ r（$φ$ twisted conjugacy类）。换句话说，这些类的组没有$ r_ \ infty $属性。 If a general automorphism $φ$ of $G\wr \mathbb Z^k$ has a finite order (this is the case for $φ$ detected in the first part of the paper) and $R(φ)<\infty$, we prove that $R(φ)$ coincides with the number of equivalence classes of finite-dimensional irreducible unitary representations of $G\wr \mathbb z^k $，由双映射$ [ρ] \ mapsto [ρ\circcφ] $（即我们证明有关这些$φ$的有限扭曲的burnside-frobenius theorem，tbft $ _f $）的猜想）。
Among restricted wreath products $G\wr \mathbb Z^k $, where $G$ is a finite Abelian group, we find three large classes of groups admitting an automorphism $φ$ with finite Reidemeister number $R(φ)$ (number of $φ$-twisted conjugacy classes). In other words, groups from these classes do not have the $R_\infty$ property. If a general automorphism $φ$ of $G\wr \mathbb Z^k$ has a finite order (this is the case for $φ$ detected in the first part of the paper) and $R(φ)<\infty$, we prove that $R(φ)$ coincides with the number of equivalence classes of finite-dimensional irreducible unitary representations of $G\wr \mathbb Z^k$, which are fixed by the dual map $[ρ]\mapsto [ρ\circ φ]$ (i.e. we prove the conjecture about finite twisted Burnside-Frobenius theorem, TBFT$_f$, for these $φ$).
