Definition:Symmetric Set

Definition
Let $G$ be a group.

Let $S \subseteq G$ such that:
 * $\forall x \in S: x^{-1} \in S$

That is, for every element in $S$, its inverse is also in $S$.

Then $S$ is a symmetric subset of $G$, or (if $G$ is implicit) $S$ is a symmetric set.

Equivalently, $S \subseteq G$ is a symmetric set iff:
 * $S = S^{-1}$

where $S^{-1}$ is the inverse subset of $S$.