分裂亚循环群的Reidemeister谱
The Reidemeister spectrum of split metacyclic groups
摘要：
给定一个群$G$和$G$的一个自同构$φ$，如果对某个$g \in G$有$x = gy φ(g)^{-1}$，则称两个元素$x, y \in G$是$φ$ -共轭的.该关系的等价类的数目是$φ$的Reidemeister数$R(φ)$。集合$\{R(ψ) \mid ψ\in \mathrm{Aut}(G)\}$称为$G$的Reidemeister谱。我们完全确定了形式为$C_{n} \rtimes C_{p}$的分裂亚循环群的Reidemeister谱，其中$p$是素数且作用是非平凡的.
英文摘要：
Given a group $G$ and an automorphism $φ$ of $G$, two elements $x, y \in G$ are said to be $φ$-conjugate if $x = gy φ(g)^{-1}$ for some $g \in G$. The number of equivalence classes for this relation is the Reidemeister number $R(φ)$ of $φ$. The set $\{R(ψ) \mid ψ\in \mathrm{Aut}(G)\}$ is called the Reidemeister spectrum of $G$. We fully determine the Reidemeister spectrum of split metacyclic groups of the form $C_{n} \rtimes C_{p}$ where $p$ is a prime and the action is non-trivial.
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