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arXiv · 2102.01027

Numbers which are only orders of abelian or nilpotent groups

Matthew Just
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Abstract

Refining a result of Erdos and Mays, we give asymptotic series expansions for the functions $A(x)-C(x)$, the count of $n\leq x$ for which every group of order $n$ is abelian (but not all cyclic), and $N(x)-A(x)$, the count of $n\leq x$ for which every group of order $n$ is nilpotent (but not all abelian).

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Matthew Just. 2021-02-01. Numbers which are only orders of abelian or nilpotent groups. https://arxiv.org/abs/2102.01027

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