$\displaystyle \gamma : G \rightarrow G$ where $\displaystyle G = (\mathbb{R},\times)$

$\displaystyle \gamma(x) = 3x$

It is trivially a bijection and $\displaystyle \gamma(x_1x_2) = \gamma(x_1)\gamma(x_2)$ seems to hold

as $\displaystyle \gamma(x_1 + x_2) = 3(x_1 + x_2) = 3(x_1) + 3(x_2) = \gamma(x_1) +\gamma(x_2)$