论文标题
有限阿贝尔群体的雷德氏频谱
The Reidemeister spectrum of finite abelian groups
论文作者
论文摘要
对于有限的Abelian Group $ a $，内态$φ$的reidemeister数量等于$ \ mathrm {fix}（φ）$的大小，这是$φ$的固定点。因此，$ a $的reidemister频谱是$ | a | $的一组除数的子集。我们充分确定了$ | a | $的reideMister频谱，即$ | a | $的分隔线作为自动形态的reidemeister数量。为此，我们讨论并证明了一个更一般的结果，可在与给定的自动形态$φ$相关的自动形态的固定点数量上提供上限和下限。
For a finite abelian group $A$, the Reidemeister number of an endomorphism $φ$ equals the size of $\mathrm{Fix}(φ)$, the set of fixed points of $φ$. Consequently, the Reidemeister spectrum of $A$ is a subset of the set of divisors of $|A|$. We fully determine the Reidemeister spectrum of $|A|$, that is, which divisors of $|A|$ occur as the Reidemeister number of an automorphism. To do so, we discuss and prove a more general result providing upper and lower bounds on the number of fixed points of automorphisms related to a given automorphism $φ$.
