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## Main Question or Discussion Point

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 g

(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 g

_{1}and g_{2}in G. g_{1}*(g_{2}*(x,y))=g_{1}*g_{2}(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.