$(\{-1,1\} \cdot)^2$ what does this notation for this group infer

Question

$(\{-1,1\}, \cdot)^2$ what does this notation for this group infer

I need to show this is isomorphic to the Klein-4 group $V_4$

the power is what throws me off. is this another way to denote $(\{-1,1,i,-i\}, \cdot)$

Or something different?

Answer 1

It would be two copies of this group - the cartesian product.

Just as $\mathbb{R}$ is the real line and $\mathbb{R}^2$ is the plane.

Answer 2

I would assume it's the group $\{ (1,1), (1, -1), (-1, -1), (-1, 1)\}$ under pointwise multiplication.

Answer 3

Literally, it's just $\{-1,1\}\times\{-1,1\}$ with tuple multiplication $\odot$ defined component-wise: $$(a,b)\odot(c,d)\stackrel{\textrm{def}}=(a\cdot c,b\cdot d).$$