# Group Norm Metric

A Group Norm Metric is a distance metric on a group ($G, +, 0$), defined by $\mid\mid x + (-y)\mid\mid= \mid\mid x - y \mid\mid$, where $\mid\mid . \mid\mid$ is a group norm on G, i.e., a function $\mid\mid . \mid\mid: G \rightarrow \mathbb{R}$ such that, for all $x, y \in G$ we have the following properties ...