Talk:Group action
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I'm not sure about the standard terminology here:
- Is it called "faithful" or "free"?
- Is "invariant" and "stable" really the same?
- Are the sets G.x really called "traces"? --AxelBoldt
- It's called "faithful", or "effective". ("Free" means that only the identity element has a fixed point.)
- I'm not sure about this one. I would use "invariant" for the sense you were talking about.
- The sets G.x are usually called "orbits" (as in the Orbit-Stabilizer Theorem).
--Zundark, 2001 Oct 28
I removed the reference to permutation groups in the first paragraph since a permutation group on M is a subgroups of Sym(M), while a transformation group G on M is given by a (not necessarily injective) homomorphism G → Sym(M). So they are not the same. AxelBoldt 17:45 Oct 31, 2002 (UTC)
There's now an overlap with orbit (mathematics).
Charles Matthews 18:52 24 Jun 2003 (UTC)
- I've now merged in that stuff. Also orbit (group theory) now redirects here. -- Fropuff 17:51, 2004 Aug 23 (UTC)