Let $R$ be a non-zero commutative ring with identity. The following is well known:

If $x,y \in R$ are idempotents then $x+y-2xy$ is also an idempotent and more than that by defining $x*y = x+y-2xy$, the set of idempotent elemetns becomes a 2-group.

Now Let $T$ be the set of all elements $x$ with $x^3 =x$. Is there any general binary operation on $T$ that makes $T$ a (semi)group ?