A remark on the number of automorphisms of finite abelian groups

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Let \mathrm{Ab}_{0} be the class of finite abelian groups and consider the function f\colon \mathrm{Ab}_{0} \to (0,\infty) given by f(G)=\lvert{\operatorname{Aut}(G)\rvert/\lvert{(G)}\rvert} , where \operatorname{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) .