Suppose a group G and it acts on a set X and a set Y. (a) A simple group action on the cartesian product would be defined as such: G x (X x Y) --> (X x Y) to prove this is a group action could I just do this: Suppose a g1 and g2 in G. g1*(g2*(x,y))=g1*g2(x). This is obvious. Basically is the proof extremely easy. I just grabbed this example out of a book and was wondering if I am close.