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arXiv · 2412.18640

A remark on the number of automorphisms of finite abelian groups

Marius Tărnăuceanu
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Abstract

Let $Ab_0$ be the class of finite abelian groups and consider the function $f:Ab_0\longrightarrow(0,\infty)$ given by $f(G)=\frac{|{\rm Aut}(G)|}{|G|}$\,, where ${\rm Aut}(G)$ is the automorphism group of a finite abelian group $G$. In this short note, we prove that the image of $f$ is a dense set in $[0,\infty)$.

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Marius Tărnăuceanu. 2024-12-24. A remark on the number of automorphisms of finite abelian groups. https://arxiv.org/abs/2412.18640

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