- #1
moo5003
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Problem:
"Let G be a group of permutations of a set S. Prove that the orbits of the members of S constitute a partition of S."
I'm a little hazy on how to start this proof. I started by writing down the definition of the Orbit of any element in S. I'm guessing, so correct me if I'm wrong that the proof should be followed by the definition of a partition and I then prove using the definition of an orbit that it fufills all parts of the definition. Or is there some type of theorem that I should spring board off of that correlates the topics.
PS: I was trying to useLagranges Theorem but that is for finite groups only, is there some other theroem I should be looking at?
"Let G be a group of permutations of a set S. Prove that the orbits of the members of S constitute a partition of S."
I'm a little hazy on how to start this proof. I started by writing down the definition of the Orbit of any element in S. I'm guessing, so correct me if I'm wrong that the proof should be followed by the definition of a partition and I then prove using the definition of an orbit that it fufills all parts of the definition. Or is there some type of theorem that I should spring board off of that correlates the topics.
PS: I was trying to useLagranges Theorem but that is for finite groups only, is there some other theroem I should be looking at?