- #1
chaotixmonjuish
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- 0
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.
(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.