仅仅是阿贝尔群或幂零群的阶数

IF 0.3 4区数学 Q4 MATHEMATICS Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI:10.5802/jtnb.1251

Matthew Just

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引用次数: 0

摘要

改进Erdős和Mays的结果，我们给出了函数a (x)-C(x)的渐近级数展开，n≤x的计数，其中每个n阶的群是阿贝尔的(但不全是循环的)，和n (x)-A(x)， n≤x的计数，其中每个n阶的群是幂零的(但不全是阿贝尔的)。

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Numbers which are only orders of abelian or nilpotent groups

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

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