Orbit of g

Hi,

I know that if G acts on set X then the orbit is
Attachment 11301

But say G=X.

Does it mean that I put two g's into the above?

Quote:

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Originally Posted by Roland25

Hi,

I know that if G acts on set X then the orbit of x is

But say G=X. Does it mean that I put two g's into the above?

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if and then clearly if is the same as multiplication operation of G, then for all

Sorry, I meant G(x) in the above.
What I mean is that if Gx={g*x : g in G}
what is Gg if g is in G.
Would it just be Gg={G} ?

Quote:

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Originally Posted by Roland25

Sorry, I meant G(x) in the above.
What I mean is that if Gx={g*x : g in G}
what is Gg if g is in G.
Would it just be Gg={G} ?

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it depends how you define the group action . if you define that for all then but if you define for all then

which is the conjugacy class of

thanks for the help so far.

I think * was multiplication in my case and so Gx=G kinda seems more appropriate.

What I still don't get however is what the actual different between Gx and Gg would be if X=G?

Say X doesn't equal G, would Gx and Gg differ then?

This is where g is in G

Quote:

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Originally Posted by Roland25

thanks for the help so far.

I think * was multiplication in my case and so Gx=G kinda seems more appropriate.

What I still don't get however is what the actual different between Gx and Gg would be if X=G?

Say X doesn't equal G, would Gx and Gg differ then?

This is where g is in G

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is fixed and is any element of this should be clear from the definition: