Notation for "absolute value" in multiplicative group. In an additive number group (e.g. $(\mathbb{Z},+)$) there is a well known notation for absolute value, namely $|a|$, which coincides with $\max(a,-a)$, for $a \in \mathbb{Z}$.
When the context is a multiplicative number group instead, is there a similar notation, which would coincide with $\max(a,\frac{1}{a})$?

If you're working with a multiplicative group $G\subseteq\Bbb{R}$, you can definitely say
$$
\operatorname{abs}(g) := \max\{g,g^{-1}\}\quad\textrm{for }g\in G.
$$
The question is whether or not it is useful to the study of the group $G$ in any way.
Also, when it comes to the question of notation, $\left|g\right|$ is normally used to mean the order of $g\in G$, which is the smallest $n\in\Bbb{N}$ such that $g^n = e$ (where $e\in G$ is the identity) or equivalently, the order of the subgroup of $G$ generated by $g$. As far as I know, there is no standard notation for $\max\{g,g^{-1}\}$ when $g\in G\subseteq\Bbb{R}$.
