Perp-structure on a group

Definition
Let $$G$$ be a group. A perp-structure on $$G$$ is defined as a symmetric binary relation $$\perp$$ on $$G$$ with the property that for any $$g \in G$$, the set:

$$g^\perp = \{h \in G \mid g \perp h \}$$

is a subgroup of $$G$$.