On the set of natural numbers which only yield orders of Abelian groups (Q1065065)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the set of natural numbers which only yield orders of Abelian groups |
scientific article; zbMATH DE number 3920590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the set of natural numbers which only yield orders of Abelian groups |
scientific article; zbMATH DE number 3920590 |
Statements
On the set of natural numbers which only yield orders of Abelian groups (English)
0 references
1985
0 references
It is shown that if f(x) is the number of integers \(n\leq x\) such that all groups of order n are Abelian and there are at least two of them, then for every positive c one has \[ x(\log \log x)^{-1}\ll f(x)\ll x(\log \log x)^{-1}(\log \log \log x\quad)^{c-1/2}. \]
0 references
Abelian groups
0 references
multiplicative functions
0 references
0 references
