My question is the following:
Suppose one has two sets $K$, $L$ and the group $W$. What is $(K \times L)/W$? Is it isomorphic to $K/W \times L/W$?
I have found something different in the literature and now I am lost.
Can anybody help me here please?
Thanks
edit: Thanks for the replies. Here it gets more precise. I have read the following: $W$ is supposed to act freely on $K$ and $L$. Its not explicitly given how it acts on $K \times L$, just that it does. Then it is given that $(K\times L)/W$ is isomorphic to $K/W \times L$ (!). In case W does not act freely on $K$, one is supposed to get $K/W \times L/(\text{stabilizergroup}(K))$.