Rational group with square-free denominators
= Rational group with square-free denominators
{title2=$\mathbb Q_{\mathrm{sq}}$}
The additive group $\mathbb Q_{\mathrm{sq}}$ consists of the <rational numbers> whose reduced denominators are <square-free integers>. If $p_0,p_1,\ldots$ lists the primes without repetition, then
$$
\mathbb Q_{\mathrm{sq}}\cong\varinjlim\left(\mathbb Z\xrightarrow{p_0}\mathbb Z\xrightarrow{p_1}\mathbb Z\xrightarrow{p_2}\cdots\right).
$$